Parallelism as a feature of Biblical exegesis has been around a long time--see this article on parallelism from the turn-of-the-century Catholic Encyclopdia, for example. Chiasmus is essentially a form of parallelism, widely celebrated in some LDS circles because it appears in the Book of Mormon as well as in the Bible. Of course, roughly ten percent of the Book of Mormon parallels selected Biblical texts verbatim and the balance exhibits notable affinities to King James Version phrasing and style, so one would think almost any Biblical stylistic feature can be found in the Book of Mormon. It's not clear why observed chiasmus really has any apologetic bite. So why is it such a hit?
First, it rewards careful reading--you can find it scattered here and there in the Book of Mormon all by yourself and feel the thrill of discovery. We are all rightly proud, I think, of the things we learn by our own study and inquiry. Second, it always gives the desired response. Observe chiasmus in a Book of Mormon passage, infer some sort of divine link to God or the Bible. If a given passage exhibits no chiasmus, is that a criticism or mark against the Book of Mormon? No, of course not. It only counts if it's there. There is no negative response. It's one of those "heads I win, tails you lose" techniques.
In fairness, Christian critics of the Book of Mormon use a variation on this approach: Any Book of Mormon passage that matches a Biblical passage is plagiarism, while any passage with no Biblical parallel is non-Biblical and therefore heretical. Another clever apologetic technique that plays well only if you are preaching to the choir.