Answers I have heard to this question:
- The Book of Mormon.
- The Bible.
- We haven't received it yet. It can't be the Bible, because it says "the mouth of a Jew", whereas the Bible came from many Jews. It can't be the Book of Mormon, because the book of Mormon came from the seed of Manasseh, not the seed of Judah.
It turns out that there is an answer to this question, and like most scriptural questions, the answer is found in the context of the quote.
The answer: "The" Jew is symbolic, not literal. The book is the Bible.
It is good to harrow up our understanding of things from time to time. In this case, we are told plainly that "the Jew" is a symbol that Nephi was shown, what "the Jew" represents, and what the book is:
19 And I, Nephi, beheld that the Gentiles that had gone out of captivity were delivered by the power of God out of the hands of all other nations. 20 And it came to pass that I, Nephi, beheld that they did prosper in the land; and I beheld a book, and it was carried forth among them. 21 And the angel said unto me: Knowest thou the meaning of the book? 22 And I said unto him: I know not. 23 And he said: Behold it proceedeth out of the mouth of a Jew. And I, Nephi, beheld it; and he said unto me: The book that thou beholdest is a record of the Jews, which contains the covenants of the Lord, which he hath made unto the house of Israel; and it also containeth many of the prophecies of the holy prophets; and it is a record like unto the engravings which are upon the plates of brass, save there are not so many; nevertheless, they contain the covenants of the Lord, which he hath made unto the house of Israel; wherefore, they are of great worth unto the Gentiles. 24 And the angel of the Lord said unto me: Thou hast beheld that the book proceeded forth from the mouth of a Jew; and when it proceeded forth from the mouth of a Jew it contained the fulness of the gospel of the Lord, of whom the twelve apostles bear record; and they bear record according to the truth which is in the Lamb of God. 25 Wherefore, these things go forth from the Jews in purity unto the Gentiles, according to the truth which is in God. 26 And after they go forth by the hand of the twelve apostles of the Lamb, from the Jews unto the Gentiles, thou seest the formation of that great and abominable church, which is most abominable above all other churches; for behold, they have taken away from the gospel of the Lamb many parts which are plain and most precious; and also many covenants of the Lord have they taken away. (1 Nephi 13)First, Nephi sees the Gentiles carrying the Bible from their captivity to the United States. He doesn't understand what that literal book is (verse 22). In response, his mentor shows him an illustrative vision. To get this conclusion, read verses 23 and 24. I have italicized the relevant parts above. In this illustrative vision, he is shown that the book came from the Jews symbolically, with a single Jew delivering the words from his mouth. It is of this book that the 12 apostles bore record. It is from the Jews (plural) that these things go to the Gentiles. We are told that these things went via the 12 apostles (verse 26).
When Nephi says "the book that preceeded from the mouth of the Jew" he is saying "the book that I saw proceed from the mouth of a Jew in my vision." This is, in effect, a title for the title-less book, not a description of how it was actually produced. He says how it is produced in 1 Nephi 13: "a record of the Jews" containing "the covenants of the Lord" and "prophecies of the holy prophets." He says it contains the same stuff as the plates of brass, just shorter.
He never indicates that this book has a single author. In fact, we are told explicitly that there are multiple authors. We are told that among the authors of this book is John the Revelator:
19 And I looked and beheld a man, and he was dressed in a white robe.Notice how he says one of the twelve apostles will write the remainder of these things. Remainder means "the rest"; what remains after some portion. John, therefore, was not the sole author of the book. This passage alone is sufficient evidence that the book that proceeds out of the mouth of the Jew does not proceed out of the mouth of a single Jew at all. Instead, the Jew is representative of a group of Jews who contributed to the book. But that isn't all the evidence.
20 And the angel said unto me: Behold one of the twelve apostles of the Lamb.
21 Behold, he shall see and write the remainder of these things; yea, and also many things which have been.
22 And he shall also write concerning the end of the world.
23 Wherefore, the things which he shall write are just and true; and behold they are written in the book which thou beheld proceeding out of the mouth of the Jew; and at the time they proceeded out of the mouth of the Jew, or, at the time the book proceeded out of the mouth of the Jew, the things which were written were plain and pure, and most precious and easy to the understanding of all men. (1 Nephi 14)