JOEL - I believe the jury is still out on this one. According to Jewish Oral Scripture, Melchizedek was the nickname for Shem the son of Noah. (Rashi, Commentaries, Genesis 14:18 - Talmud, Tr. Nedarim p. 32)
(See also Historical Research on the Interpretations on the Person of Melchizedek)
A scripture from the Book of Jasher would seem to concur:
"And Adonizedek(Melchizedek) king of Jerusalem, the same was Shem, went out with his men to meet Abram and his people, with bread and wine, and they remained together in the valley of Melech. And Adonizedek(Melchizedek) blessed Abram, and Abram gave him a tenth from all that he had brought from the spoil of his enemies, for Adonizedek(Melchizedek) was a priest before God. (Jasher 16:6-12)

And according to the Times and Seasons, a Nauvoo newspaper, some early LDS leaders also believed that Melchizedek was Shem:
"And with the superior knowledge of men like Noah, Shem, (who was Melchisedec) and Abram, the father of the faithful,"(T&S 5:746).
However, even though Shem is identified as a great high priest (D&C 138:41), it would appear from Doctrine and Covenants 84:14 that the two might not be the same individual:
"Which Abraham received the priesthood from Melchizedek, who received it through the lineage of his fathers, even till Noah" (D&C 84:14)
The word "fathers"(plural) would mean that there must have been at least two generations between Melchizedek and Shem. (See also Mormon Doctrine p. 475) Fortunately our eternal life is not dependent on knowing bits of Bible trivia such as this.