In what language was the Book of Matthew written?

I have heard it taught in several places that Matthew was originally written in Hebrew and its intended audience was the Jews (which would help explain why it seems a bit more vague on key Christian concepts). But recently I have been told that there are no Hebrew manuscripts of this text. I assume at least that the person who told me this meant that there are no Hebrew manuscripts that outdate the Greek ones. So in what language was Matthew written?