I have a hard wired smoke detector with no battery backup that started chirping. I turned off the breaker and it stopped for a while but now still chirps about every 60 seconds. We installed a new detector, still chirps. We removed the new detector, still chirps. Any ideas?

Either you have a serious situation in your home or there has to be a battery someplace in this problem.

With the breaker in the OFF position, can you take a voltage reading at the alarm's outlet box?

Look again. Never saw a hard wired detector that didn't have a battery back up. In addition to the 9 volt back up battery there is an additional internal rechargeable battery that sounds the alarm when the 9 volt battery is discharged.

This may help.

How to Stop a Hard-Wired Smoke Alarm From Chirping | eHow

My Smoke Detector Does Not Have Battery Backup & Is Chirping | eHow

I clean mine twice a year, you wouldn't believe the dust build up. I also bought two newer battery ones to supplement the hard wired one since power outages are common in my area.

You may well indeed have an electrical issue that needs addressing by a professional electrician as I have learned when the detectors went out and the problem was traced to a faulty device on the same circuit (door bell transformer). Don't hesitate to be willing to look deeper and consult at least with a more knowledgeable professional.