Aye, Aye, Captain!

I heard the word, “aye,” today on a tape (audiobook, of course). It's an interesting word. I think every American knows what it means. But why do sailors, pirates, and the crew of the Enterprise, use a word which must be Gaelic in origin? Were the earliest sailors Gaelic?

Also used in parliamentary settings, when you have to vote either aye or nay.

Am I wrong in thinking this is Gaelic or Celtic? I know I’ve heard actual Irish-Americans say this. The dictionary doesn’t give me an etymology. I’ll have to refer to the HUD (huge unabridged dictionary), and get back to ye.
In the meantime, Top o’ the mornin’ to ye!