I've been to a few dinner parties where they've had private chefs. It is a great idea.

One of my girlfriends always has a chef and wait staff for all her parties, for simple get-togethers she just has wait staff, they clean up as they go along and leave the place tidy, only stuff she has to worry about is what mess is made after they leave.

For the chef it is probably per head dependant on how many people you are having, for wait staff (which I'd advise to have) it is a per-hour cost with a minimum amount of hours.