At what time will the chef arrive for a private chef service ?

On average 2 hours before the actual meal time. However, for certain type of services, the chef will arrive earlier.

The equipment in your kitchen will also determine the arrival time. If your kitchen isn't very spacious or doesn't offer much equipment, the chef will do most of the preliminary work in his own work place and finalize the dishes at your home. Therefore, there will be no need for him (or her) to arrive earlier at your home. 
Whatever happens, the chef will contact you after you made a booking and tell you at what time you should expect him. If you cannot be there well ahead, just advise him and the chef will work it out!