A chemical peel uses acids to destroy the epidermis and parts of the dermis. During the initial recovery period, the skin undergoes a process of 'epithelialization,' whereby new skin is created to cover the treated areas.
During the initial healing phase, it is wise to avoid any harsh chemicals to the skin. The appropriate length of time is more an academic issue but the practical aspects of chemical peeling mandate that you err on the side of being conservative.
Common chemical peels are glycolic acid, salicylic acid, retinoic acid, and trichloroacetic acid.