I think you should take your kitty to the vet first to rule out any bugs or skin conditions and/or painful problems that might be causing obsessive licking.
If that doesn't turn up anything my second thought would be a feliway plugin. If you just got your kitty then she/he(?) might be stressed out by the move and the new space and be showing this stress by licking. The plugins and the spray are available online, in Petsmart or perhaps through your vet. Here's their homepage.http://www.feliway.com/homefeliway.nsf
The last suggestion... my cat does this too and I belive it's caused by an allergy to her food. I have the feliway plugin and I feed her "Wellness" food, an all organic mix. It's been an uphill road with her but the plug in and new food seems to be helping.
Good luck and keep us updated on what happens!