A light chemical peel will not cause hair loss. If the peel was too deep and caused blistering and scarring, it could lead to damage of the hair follicles in the area with resultant hair loss.
In general, facial peels should not interfere with hair growth. The hair follicle originate deep under the skin, and the peels act on the superficial layers of the skin. There may be a few follicles that are affected mechanically (the rubbing of the skin) but not necessarily chemically.