I am having this same issue with my 2008 Equinox. If the interior lights come on before opening any doors as I take the key out of the ignition, it doesn't chime. But if they don't come on, it chimes fast when the door is opened. There is a certain clunk noise when turning it off too when it's okay. I keep turning the key back and forth, sometimes restarting the car until it finally makes the clunk sound & the interior lights come on. Only then does the door chime not go off as I open the door. Dealer said it had to do with the ignition assembly & it'd be $600+ to fix. I'll keep listening for the clunk!!