Some very good advice here.
I highly recommend discussing the problems with the offending player before resorting to a "booting". As many others have said, be honest and up front, and do it as soon as possible. When discussing, I'm surprised this hasn't been mentioned more often: use specific examples . The "whys" are so important here.
Just using a nebulous statement such as "we don't have chemistry" will surely result in more hard feelings than is necessary. Specific examples will show exactly what you have problems with, and gives the offending player a chance to rectify his/her behaviour (or at the very least, improve his/her understanding of the situation). "This is how we play, this is what you do, this is why it causes these particular problems."
Once the specific problems have been discussed, and the offending behaviour continues, then asking the player to leave can be done much more easily. Again, honest and direct, using examples from the previous discussion. Referring back to the previous discussion (highlighting the problems that were occuring) will make dismissal easier. Stick with the facts, don't get emotional, and be very polite. (You don't have to be *overly* direct, or blunt, or rude to get your point across.)
Rational discussion highlighting specific examples of problems and conflicting play styles (and their consequences) goes a long way to diffusing a possible volatile situation.
Edit:
Conflict-resolution at places of work is much the same way, and has worked well in the past. Oh, and what a previous poster mentioned: taking the high road with the "it's not you, it's me" approach is also very good.