Sounds like there is a problem with the extractor and/or the chamber is too tight, that is assuming the spent casing is not ejecting. The slide is at least cycling after firing the first shot, correct?
New or used gun?
How long have you had it?
Factory ammo or reloads?
Can you post pictures of the extractor hook?
Can you post picures of the spent brass after they are removed from the chamber, particularly the rim?
1st suggestion is to call Kimber and sned it in for warranty service.
2nd suggestion is to take to to a qualified gun smith with good 1911 experience.
3rd suggestion is to sell / trade it as is, giving full disclosure to the new buyer/owner etc.
4th suggestion is to foolishly keep trying to meet the 500 rd break in guide lines in the user's manual...yeah, lets not do that.
5th suggestion is for you to try and figure it out on your own asking a bunch of guys on the interenet for help, this is more fruitful than option 4, but 1-3 are better choices in the long run.
How much time, money, and effort are YOU willing to put into a gun that should be fixed by the manufacturer?