I had a similar problem with my i12060CA with 2 alarms interconnected over AC as well as 9v battery backup. It was a professional installation over 1 year old that had been working and tested with real kitchen smoke so I knew the interconnected AC wiring was installed correctly. Then after 1 year they started chirping and no matter what I did it would not shut up! I changed the battery with the exact Duracell  MN1604 model recommended in the manual, tested the batteries with my multimeter, cleaned the device with compressed air, all to no avail.

I wish Kidde had the reset instructions in the manual for the i12060CA, they don't. I followed the suggestion on a forum of resetting it by unplugging AC and removing battery and then holding down the TEST button for 1 minute. Someone on another forum had suggested 15 seconds but that was not enough. For good measure the second time around I left it disconnected for 10 minutes before popping the battery back in and then reconnecting to AC and testing with the TEST button. Chirping has stopped! Testing has passed and indicator lights are properly indicating solid GREEN for AC power connection and intermittent short RED flash for active unit, with no chirping.

When holding down the TEST button for 1 minute it sounds like you are killing a small helpless electronic animal. I assume we are using the test feature and speaker to drain the remaining charge stored in the capacitors on the circuit board. This is why I also left it for a couple of minutes before hooking up, just to be sure. Also note there seems to be some indication in forums that it matters what order the AC and battery power are connected. Not sure if this is just a myth but suggestion was to connect battery first and then AC. Seems odd since the device was designed to change the battery while still connected to AC but I followed that process as well as the reset so I'm mentioning it here.

If your unit is battery only I understand this reset process will also work.

Please note that this was not a process recommended by Kidde support, but rather found in online forum posts made by other non certified humans, so use at your own risk and discretion.