We have had one of our hardwired AC/DC First Alert Smoke Detectors chirping for 17 days straight now - sometimes for an hour or hours before a break. The Electrician has visited our house every single day except Sunday and replaced all 7 units twice. The Electrician has them on the same circuit as 3 of our rooms - if I totally disconnect the smoke alarms, we lose power to clocks, lights, and fans in Great room, bedroom, and TV room. AND, if I remember correctly, when we threw the breaker on it, the chirping continued even when disconnected and battery pulled out of it - the ceiling chirps! The Electrician told us that couldn't happen - and then it happened in front of him. He gave a lame excuse that it must be another one doing it but couldn't not find it. We are going crazy - thinking about renting a hotel room to get some sleep and charging it to the builder. House is only 2 years old. Yes, batteries where changed out in March 2014 and the problem started August 16, 2014. No problem at all until 8/16/14. Now we have nothing but problems!

if I totally disconnect the smoke alarms, we lose power to clocks, lights, and fans in Great room,
That is not logical. You should be able to unplug the smoke detectors with out interrupting anything. That however will not stop the chirping, the battery charges another internal battery (I think it is really a capacitor) and that power for the chirping. It will eventually run down also.

The chirping is an signal of low battery. Since you say you replaced the batteries, I suggest you look for another smoke detector somewhere that you may not be aware of. Such as in the attic.