I am baffled by your initial response. This is the hospitality business. You have a place that is in the $600 a night range. Anyone who can afford this might want any number of services on-site. I can imagine a yoga instructor, massage therapist, golf coach, and yes, a private chef.
If I were you, I would say "absolutely" and then require proof that the private chef has all the required permits and licenses, and get a copy of their insurance that protects you should something go wrong. You could even require that the chef bring all the dishes, silverware, cooking implements, etc., and when these folks are done, I would put together a list of area vendors that you are comfortable having on your property.