Had the same problem and at the same time I had my Multi-Function switch ketching on fire.
Found out, how the chime works when the key is inserted into the lock cylinder, the one side of the cylinder has a positive lead coming to it. The other side has a pickup or ground lead. When you insert the key, you complete the connection. What probably happen is that your pickup lead broke of and is wedged itself inside of the lock cylinder to ground itself out hence making the chime go off all the time. Your in luck, I got pictures because I was going to write a how to but never got around to it. Mine doesn't ding at all now when I leave the key in the ignition.
I'll guide you through how to fix it, its really easy.
1. You must remove the Tilt Leaver, should be able to put a crescent wrench on it and unscrew it.
2. Next you must unscrew the 4 bolts holding the two plastic neck peaces to one another. (Larger hole of the two in the picture below)
3. Next we need to remove the lower portion of the plastic neck, which will involve removing the lock cylinder. This is quite simple, grab a very tiny flat blade screw driver. Your also going to need your keys for this. Insert you keys turn the vehicle to the ON position, which is position 2, the one right before the start position (we don't want to start the vehicle)
** Should be in this position...
This sets up the lock cylinder for removal. To remove the lock cylinder, insert your small flat plade screw driver in the smaller of the two holes in the picture below.
There should be enough room that will allow you to pull down the black plastic piece to see a small hole in the bottom of the lock cylinder. There is a ball bearing in there you want to press in with your flat blade screw driver. When you do, the lock cylinder and keys should pull straight out. Hardest part is done now....
4. You should see a loose wire or a wire on the bottom portion of the lock cylinder socket, it should have a gray clip around it. Mine was hanging freely from me pulling out the lock cylinder.
5. All we have to do now is bend that copper tab back and warp electric tab around it so it does not ground out on anything else inside the steering column. An just tuck it back inside the steering column somewhere.
6. Reinstall the lower portion of the steering column neck with the four screws.
7. To put the lock cylinder back in, all you need to do is line up the groves and insert it stright in and the turn it back to off. Remove keys
All done! Now you will have no chiming when the keys are left inside the lock cylinder. Now it will still chime if you have it in the Accessory position and open the drivers door.
Good Luck, ask me any questions you need. Sorry I did this off the top of my head in about 15mins...lol