How old is it? They start chirping after a set number of years when they are at the end of their useful life.
I would buy a replacement for the whole thing. They are not that expensive. We had the same thing happen with ours and had to replace them.
Be prepared to replace all of them... they were installed the same day and so are all the same age.
We had the same issue -- ultimately had to turn off power via circuit breaker and then turn it back on so the thing reset or something.
This is an apartment building so I have no idea if this will work for you but it may be worth a try.
WTF? It's driving me insane. It chirps every 60 seconds. I'm at a loss.