Chiasmus is a rhetorical device whereby the arrangement of words in one clause mirrors the arrangement of words in a preceding or proceeding clause. In the first clause of Brutus's plea, he says, "Believe me for mine honor," and in the second clause he says, "and have respect to mine honor that you may believe." In other words, he asks his audience first to believe that he is honorable, and then to believe him because he is honorable. The second clause essentially repeats the idea contained within the first. In the above quotation, we can see that the order of the words "believe" and "honor" in the first clause is reversed in the second. This symmetrical structure of chiasmus gives to the lines a pleasing, satisfying sense of neatness, and completeness.
It would be easy to mistake this example of chiasmus for an example of antithesis. Indeed, in both devices a sentence has two separate but related parts. In chiasmus those two parts are mirror images of one another, and each part reflects the same idea that is contained in the other. In antithesis, however, the two parts of the sentence are not reflections of one another, but instead contrast one another. Chiasmus is used to emphasize similarity, and antithesis is used to emphasize difference. One famous example of antithesis, for example, is the opening line of Charles Dickens's novel A Tale of Two Cities: "It was the best of times, it was the worst of times."