I've seen a lot of threads on here about problems with the door ajar light staying on, but not just the chimes. In those instances it seems to help by spraying some WD40 on the door hinges or latches. Not sure if that will help you or not, but may start the troubleshooting process.
Hope it helps.
02 Ranger XLT 4x4 Off Road, 4.0L SOHC, Automatic, 8.8 4.10 LS, Super-Cab, 3" Body Lift, 33x12.5x15 BFG All Terrains on 15x8 M/T Classic IIs, 5K 55w Heads, 5K 35w fogs, custom front skid plate, various other goodies.