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Question: When did Joseph Smith receive the revelation on plural marriage?
Question: When did Joseph Smith receive the revelation on plural marriage?
Joseph's first introduction to the concept of plural came during the 1829 translation of the Book of Mormon
Of the little we do know, much comes from later reminiscences. Later memories are not useless, but memory can change, and can be influenced by what people later came to believe or desire. Such data must be used with caution.
There are enough scattered bits of evidence, however, that let us form some tentative conclusions.
The first specifically-LDS encounter with plural marriage was the 1829 Book of Mormon. The prophet Jacob rebuked the Nephites for their practice of having many wives and concubines. Jacob forbade this practice, and declared monogamy to be the norm unless "I will…raise up seed unto me…." 
It is not clear that the early Saints contemplated any exceptions to this command in their own case, until after Joseph had taught plural marriage. As late as May 1843, Hyrum Smith (not yet converted to Joseph's plural marriage doctrine) attempted to rebut rumors of plural marriage by citing the condemnation in Jacob 2. 
Evidence points to a 1831 date for the revelation to Joseph regarding plural marriage
There are no contemporaneous records which tell us when Joseph first taught plural marriage, or when he first had a revelation endorsing it. One account has Brigham Young placing the revelation to Oliver Cowdery and Joseph Smith in 1829 while translating the Book of Mormon. 
Most scholars have rejected this early date. Brigham was not even a member at this time, so he would have heard such a story second-hand at best, and may well have misunderstood the timing. There is nothing in the Book of Mormon that portrays plural marriage positively, so there is little which would inspire Joseph and Oliver to ask questions about it, and such questioning seems to have been a prerequisite to Joseph and Oliver's early revelations on baptism, the priesthood, and other matters. The journal which records the 1829 date may be in error, since there is another, earlier record in which Brigham Young opines that Joseph had the plural marriage revelation "as early as in the year 1831." 
Other evidence also points to an 1831 date. Joseph undertook his revision/translation of the Bible, and was working on Genesis in February–March 1831.  Hubert Howe Bancroft was the first to suggest this theory,  while Joseph Noble,  B.H. Roberts,  and Joseph F. Smith  have agreed. The obvious approval of the polygamous patriarchs in Genesis is a more likely stimulus for Joseph's questions to the Lord about plural marriage than the Book of Mormon's generally negative view.
Joseph was probably teaching the idea of plural marriage to a limited circle by the end of 1831
The date of 1831 is reinforced by a letter written years later by W.W. Phelps. Phelps reported that on 17 July 1831, the Lord told Joseph "It is my will, that in time, ye should take unto you wives of the Lamanites and Nephites, that their posterity may become white, delightsome and just." Phelps then said that he asked Joseph three years later how this commandment could be fulfilled. Joseph replied, "In the same manner that Abraham took Hagar and Keturah; and Jacob took Rachel, Bilhah and Zilpha, by revelation.”  Phelps' recollection is reinforced by Ezra Booth, an apostate Mormon. In November 1831, Booth wrote that Joseph had received a revelation commanding a "matrimonial alliance" with the natives, though he says nothing about plural marriage per se. 
Since Joseph's explanation to Phelps came three years later, this does not help us date the receipt of the revelation specifically. It may be that Joseph did not understand the import of the July 1831 revelation any more than Phelps did. On the other hand, Orson Pratt reported that Joseph told some early members in 1831 and 1832 that plural marriage was a true principle but that the time to practice it had not yet come.  Lyman Johnson also reportedly heard the doctrine from Joseph in 1831,  as did a plural wife who recalled late in life that in 1831 Joseph told her that he had been commanded to one day take her as a plural wife.  Mosiah Hancock reported that his father was taught about plural marriage in the spring of 1832. 
Some authors have suggested that Phelps' late recollection is inconsistent with other things that he wrote earlier. Richard Van Wagoner argues that:
the Phelps letter has been widely touted as the earliest source documenting the advocacy of Mormon polygamy, [but] it is not without its problems. For example, Phelps himself, in a 16 September 1835 letter to his wife, Sally, demonstrated no knowledge of church-sanctioned polygamy: "I have no right to any other woman in this world nor in the world to come according to the law of the celestial kingdom.” 
It seems, though, that the problem is more in Van Wagoner's reading of the data. Phelps says nothing about "church-sanctioned polygamy," one way or the other. He merely tells his wife that he has no right to any other woman. This was certainly true, since Joseph Smith had introduced no other men to plural marriage by September 1835. In fact, Phelps' remark seems a strange comment to make unless he understood that there were circumstances in which one could have "right to" another woman. 
Joseph F. Smith gave an account which synthesizes most of the preceding data:
The great and glorious principle of plural marriage was first revealed to Joseph Smith in 1831, but being forbidden to make it public, or to teach it as a doctrine of the Gospel, at that time, he confided the facts to only a very few of his intimate associates. Among them were Oliver Cowdery and Lyman E. Johnson, the latter confiding the fact to his traveling companion, Elder Orson Pratt, in the year 1832. (See Orson Pratt's testimony.)" (Andrew Jenson, The Historical Record 6 [Salt Lake City, Utah, May 1887]: 219) 
The bulk of the evidence, therefore, suggests that plural marriage was known by Joseph by early 1831. The Prophet was probably teaching the idea to a limited circle by the end of that year.
- Jacob 2:27–30.
- Levi Richards Journal, 14 May 1843; cited by Richard S. Van Wagoner, Mormon Polygamy: A History (Salt Lake City: Signature Books, 1989), 54.; Linda King Newell and Valeen Tippetts Avery, Mormon Enigma: Emma Hale Smith, 2nd ed. (Urbana, Illinois: University of Illinois Press, 1994), 141, 332.
- Brigham Young, quoted in Charles L. Walker, "Diary," (Harold B. Lee Library, BYU, 1855–1902), 25–26.
- Journal History, 26 August 1857; cited by Hyrum Leslie Andrus, Doctrines of the Kingdom (Salt Lake City, Utah: Desert Book Co., 1999), 489n436.
- Robert J. Matthews, "A Plainer Translation": Joseph Smith's Translation of the Bible, a History and Commentary (Provo, Utah: Brigham Young University Press, 1975), 64–67. Also discussed in Danel W. Bachman, "A Study of the Mormon Practice of Polygamy before the Death of Joseph Smith" (Purdue University, 1975), 67 and Danel W. Bachman, "New Light on an Old Hypothesis: The Ohio Origins of the Revelation on Eternal Marriage," Journal of Mormon History 5 (1978): 24. This view is endorsed by Todd Compton, "Fanny Alger Smith Custer: Mormonism's First Plural Wife?," Journal of Mormon History 22/1 (Spring 1996): 178–181.
- Bachman, "New Light on an Old Hypothesis," 22n11 notes that Roberts' History of the Church introduction (5:xxix) and Hubert Howe Bancroft, History of Utah (San Francisco: A.L. Bancroft Co., 1889), 161 were the first to posit the role of Joseph's revision of the Bible in the plural marriage revelation.
- Joseph Noble, cited in Millennial Star 16:454.
- Joseph Smith, History of the Church of Jesus Christ of Latter-Day Saints, ed. Brigham H. Roberts, 7 vols. (Salt Lake City, Utah: Deseret Book Company, 1980), 5:xxix.
- }Joseph F. Smith at funeral of Elizabeth Ann Whitney; cited in Deseret Evening News (18 February 1882).
- W.W. Phelps, Letter to Brigham Young, 1861, original in Church Archives, emphasis in original; cited by B. Carmon Hardy, Doing the Works of Abraham: Mormon Polygamy: Its Origin, Practice, and Demise, Kingdom in the West: The Mormons and the American Frontier (Norman, Okla.: Arthur H. Clark Co., 2007), 36–37
- Ezra Booth, Letter to the editor, Ohio Star (10 November 1831).
- Orson Pratt, "Celestial Marriage," Journal of Discourses, reported by David W. Evans (7 October 1869), Vol. 13 (London: Latter-day Saint's Book Depot, 1871), 192–193.
- Lyman Johnson as recounted by Orson Pratt, reported in “Report of Elders Orson Pratt and Joseph F. Smith," Millennial Star 40/50 (16 December 1878): 788; cited in Bachman, "Mormon Practice of Polygamy", 56.
- Mary Elizabeth Rollins Lightner to Emmeline B. Wells, Summer 1905, LDS Archives; cited by Newell and Avery, Mormon Enigma, 65.
- Todd Compton, In Sacred Loneliness: The Plural Wives of Joseph Smith (Salt Lake City: Signature Books, 1997), 644. ( Index of claims ); citing Mosiah Hancock Autobiography, 61–62.
- Richard S. Van Wagoner, Mormon Polygamy: A History (Salt Lake City: Signature Books, 1989), 3n2.
- Phelps would publicly teach the idea of eternal marriage soon thereafter: "[W]e came into this world and have our agency, in order that we may prepare ourselves for a kingdom of glory; become archangels, even the sons of God where the man is neither without the woman, nor the woman without the man in the Lord…" - WW Phelps to O[liver] Cowdery, "Dear Brother in the Lord," Latter-day Saint Messenger & Advocate 1/9 (June 1835): 130. See discussion of the Phelps material in Bachman, "New Light on an Old Hypothesis," 28–29
- Joseph F. Smith (comment made 4 March 1883) in "Utah Stake Historical Record, 1877–1888," LDS Archives;Richard and Pamela Price, Joseph Smith Fought Polygamy—Vision Articles [from Vision Magazine, Vol. 32–46, 48–51, 53–56], vol. 2 (E-book: Price Publishing Company, n.d.), "LDS Leaders Accused Oliver Cowdery of Polygamy".