Can chemical peels erase fine lines and wrinkles?

Improve, not erase. Chemical peels, dermabrasion, and laser resurfacing can all improve fine lines and wrinkles. Why? Because they are all varieties of controlled burns. They cause a superficial injury to the skin, so when it heals it tightens (because scars contract) and this tightening improves fine lines and wrinkles.
Yes. Depending upon the type of peel and how deeply it is performed, chemical peels can markedly decrease fine lines and wrinkles. Just make sure you choose someone experienced to perform the peel as certain skin types may react poorly to a peel and there is always the possibility of complications. An experienced doctor will know how to screen patients properly and handle any problems that arise.