If you really mean one that physically attaches to the clock, then that's a contact microphone. That type will pick up all the whirrs, clicks and bangs of the internal workings of the clock, as well as the chimes. Maybe that's what you want, but if you want to record the sound of the clock as we hear it, you need a standard microphone. It's difficult to recommend a type or model of either sort until we know what recording equipment you have for the microphone to plug into, and the sort of room you have available to make the recording in.

Thanks Boswell, it's a good place to start.