LDS scholars also point out that this style was not identified as chiasmus until after the time of Joseph Smith. Thus, they reason, his use of it in the Book of Mormon demonstrates that it is a translation of an ancient text. However, a brief investigation shows there are other explanations.
First, this poetic style has always been in the Bible. In Joseph Smith's day this was usually referred to as parallelism.
In the October 1989 Ensign article, "Hebrew Literary Patterns in the Book of Mormon," there is mention of a book on Hebrew poetry, dated 1787, which discusses the poetic style of parallelisms. The term chiasmus is never used, but this book clearly shows that Hebrew poetic styles were recognized and studied even before Joseph Smith's time.
LDS scholar Blake Ostler, in reviewing the book, Book of Mormon Authorship: New Light on Ancient Origins, commented:
Book of Mormon Authorship has made a prima facie case for the ancient origins of the Book of Mormon. It fails, however, to respond to scholarly criticism in some crucial areas. For example, since Welch first published his study on chiasmus in 1969, it has been discovered that chiasmus also appears in the Doctrine and Covenants (see, for example, 88:34-38; 93:18-38; 132:19-26, 29-36), the Pearl of Great Price (Book of Abraham 3:16-19; 22-28), and other isolated nineteenth-century works. Thus, Welch's major premise that chiasmus is exclusively an ancient literary device is false. Indeed, the presence of chiasmus in the Book of Mormon may be evidence of Joseph Smith's own literary style and genius. Perhaps Welch could have strengthened his premise by demonstrating that the parallel members in the Book of Mormon consist of Semitic word pairs, the basis of ancient Hebrew poetry. Without such a demonstration, both Welch's and Reynold's arguments from chiasmus are weak (Dialogue: A Journal of Mormon Thought, Vol. 16, No. 4, Winter, 1983, p. 143).
Second, as Ostler pointed out, the Doctrine and Covenants has examples of the same pattern. Since Joseph Smith dictated the revelations in the Doctrine and Covenants, and it is not claimed that they were translations of ancient writings, obviously this pattern was part of Smith's style. The Pearl of Great Price and Joseph Smith's diary exhibit similar patterns.
A thesis at BYU by Richard C. Shipp, "Conceptual Patterns of Repetition in the Doctrine and Covenants and Their Implications" (Masters Thesis), arrives at a similar conclusion. Although Mr. Shipp was not trying to disprove chiasmus claims in the Book of Mormon, his study shows that Joseph Smith had picked up both the rhythm of chiasmus and parallelism. In his 1832 first vision account, Joseph claimed that he had studied the Bible since he was twelve, so it is quite conceivable that he picked up this style from his studies.