The term chiasm comes from the Greek letter chi, which looks like our letter X. A chiasm (also called a chiasmus) is a literary device wherein a sequence of ideas is presented and then repeated in reverse order, frequently used to emphasize the idea at the center. This results in a "mirror" effect as the ideas are "reflected" back in the passage. It is similar to a palindrome, a word or phrase that can be read forwards and backwards (e.g., deed, civic, kayak, level, racecar, rotator, Hannah, "Was it a rat I saw?"). Each idea is connected to its "reflection" by a repeated word, which is often in a related form.
The structure of a chiasm is typically expressed via a series of letters, with each letter representing a new idea. The first idea corresponds to the last idea, the second idea corresponds to the second last idea, the third idea corresponds to the third last idea, etc. For example, the structure ABCCBA refers to three ideas (A, B, and C) repeated in reverse order (C, B, and A). Chiasms frequently include a main idea in the middle of the repetition, which by virtue of its location is emphasized. The structure ABCXCBA has the three ideas (A, B, and C) repeated in reverse order, but a fourth idea is inserted before the repetition (X). The middle idea is the central point of the chiasm, the main focus. It is what all the other ideas are pointing to.
The motto of Alexandre Dumas' Three Musketeers, "All for one, and one for all," is a basic chiasm. The words all and one are repeated in reverse order in the second half of the sentence. The same goes for the common saying "When the going gets tough, the tough get going." Benjamin Franklin's axiom "By failing to prepare, you are preparing to fail" is a chiasm, as is John F. Kennedy's "Ask not what your country can do for you, ask what you can do for your country." Some chiasms are so complex that they span entire poems. (Palindromes can do the same thing, as seen here.)
The letter to the Colossians is filled with chiastic structure. An example is 1:15-20.
A (1:15-16) — Everything in heaven and earthB (1:17-18) — He is the head of the body, the churchA (1:19-20) — Everything in heaven and earth
There are many examples of chiasms in the Bible. Jesus' words in Mark 2:27 are in the form of a chiasm: "The Sabbath was made for man, and not man for the Sabbath." Genesis 6-9, Joshua 1:5-9, Isaiah 1:21-26, Ecclesiastes 11:3-12:2, Amos 5:4-6a, and Matthew 23:12 are other examples of chiasms. Joel 3:17-21 is an example of a longer chiasm, having seven parts, much the same as the chiasm found in Daniel 9:25-27.
Viewing Daniel 9:25-27 in this way clarifies a great deal of confusion. The last part of verse 27 describes the destruction of Jerusalem, which corresponds to its construction in the beginning of verse 25. The he in the first part of verse 27 quite obviously corresponds to the Messiah in the second part of verse 25. The death of the Messiah is the great focus of this prophecy as His death would make atonement for all evil and, as a result, bring in everlasting righteousness (v. 24). Understanding this chiasm does away with the false interpretation imposed on this passage by Dispensationalists.