In considering this question, particular regard should be given to a chiasmus appearing at a very important hour in the Book of Mormon timeline. In between the time of the great destruction that befell the Nephites following Christ's death and His postmortal appearance and ministry among them, this chiasmus comes by His own voice:
D O ye people of these great cities which have fallen,
C who are descendants of Jacob, yea, who are of the house of Israel,
B how oft have I gathered you as a hen gathereth her chickens under her wings,
A and have nourished you.
B' And again, how oft would I have gathered you as a hen gathereth her chickens under her wings,
C' yea, O ye people of the house of Israel, who have fallen; yea, O ye people of the house of Israel,
D' ye that dwell at Jerusalem, as ye that have fallen;
(3 Nephi 10:4-5, ending partway through verse five)
I've underlined other repeating phrases that would either justify an alternative dissection or an outright rejection of this passage as a chiasmus (sometimes a chiasmus is too easy to come by when so many repeating/parallel phrases occur). This dissection feels right to me, though; notice in both "C" lines, the Lord twice states he is addressing the house of Israel ("descendants of Jacob" is synonymous). Also, the central focus, the "nourishment" that comes from the "true vine" (see 1 Nephi 15:15), is consistent with the Christ-centered central themes of other chiasmi in the Book of Mormon.
It should be also be noted that "gathered you as a hen gathereth her chickens" repeats yet twice more in the remainder of verse five through six, though its usage changes a little; now the phrase is followed each time by an action (or reaction) on the part of the house of Israel ("and ye would not," "if ye will repent..."). It may seem odd that a chiastic device would include only the first two repetitions of this phrase and leave out the latter two. They, however, may be part of another smaller chiasmus (starting with line D' again and relabeling it line c):
c1 ...ye that dwell at Jerusalem,
c2 as ye that have fallen;
b1 yea, how oft would I have gathered you as a hen gathereth her chickens,
b2 and ye would not.
a O ye house of Israel whom I have spared,
b1' how oft will I gather you as a hen gathereth her chickens under her wings,
b2' if ye will repent and return unto me with full purpose of heart.
c1' But if not, O house of Israel, the places of your dwellings
c2' shall become desolate until the time of the fulfilling of the covenant to your fathers.
(3 Nephi 10:5-7)
This dissection is somewhat more debatable, especially the parallels between the "c" lines. However, as with the previous chiasmus, the central focus is the Lord's hand in the lives of His people--again, consistent with other Christ-centered central themes elsewhere.
Assuming my proposal on either chiasmus is correct, why does the Lord use this device at such a critical hour? Is He merely speaking to the Nephites "according to their language" (see 2 Nephi 31:3)? Or did He even have those present in mind when He used this device? (Given their astonishment at both the destruction they had just faced and the voice they were now hearing, do you think anyone said, "Gee, he's using a chiasmus, isn't he?")