Catholic apologists like to argue this, mostly to bolster their argument for the word petra (Aramaic, cepha) in Matthew 16. There is a statement by Papias that some believe indicates that Matthew was originally written in Aramaic (although even the interpretation of that statement is the subject of dispute), but there is contradictory evidence from the Greek text itself. First, there are no ancient Aramaic copies of Matthew, but plenty of Greek copies. Second, when a document is translated from a source language to a receptor language, the receptor language usually gives tell-tale indications that it is a translation. For instance, it will typically incorporate common idioms from the source language, and translate them in a woodenly literal way. We don't find that phenomenon in the Greek text of Matthew's gospel. Third, when Matthew quotes the OT, he often uses the Greek Septuagint rather than the Hebrew text. If Matthew was originally written in Aramaic, he certainly would have used the Hebrew OT consistently, but he doesn't. The OT quotes we find are either Matthew's Greek translation of the Hebrew, or taken straight from the Greek Septuagint--not Greek translations of an Aramaic rendition of the OT. As D. A. Carson says in his commentary on Matthew: "It remains linguistically improbable that the whole of Matthew was originally in Aramaic" (15).

E.S.