Greek musicals?

Today, my friend Natalie invited me to go see a Broadway singer who was playing at the Hersheypark amphitheatre. Unfortunately, I could not attend, but the word amphitheatre made me think of Greek theatre. I wonder if there were any Greek plays that incorporated musical elements. Maybe there are some parts where the characters or the chorus could sing their lines in order to get their message across in a different, but still effective manner. Just something to think about...