Plumbing Questions? Ask a Plumbing Expert.
Make sure the room the water heater is in, is well ventilated, then un plug the water heater, wait 5 minutes, then plug it in again, and tell me if the chirping stops and if the water heater fires... that is called a 'soft reset procedure'. The chirping could be caused by a combustible vapor sensor fit onto some models.
We can go from there.