Hen is crowing like a rooster...at 5 am

We lost our "top hen" last month, and as the pecking order re-established, our new top hen has taken to giving a warbling cock-a-doodle-doo at 5 in the morning! Still laying fine though. I've looked on the Internet (backyard chickens, etc) for how to deal with this, but can't seem to find whether suggested solutions will lead to permanent behavior change (eg keep them in a small pet carrier overnight so they can't raise their neck up to crow). Anyone have any experience or suggestions on this? We'd like to keep the bird, but I bet our neighbours don't at this point!