Chemical peels are natural

Just remember that glycolic acid, the most common peel, is derived from sugar cane.  Lactobionic and lactic acid peels are from milk sugar (lactose) and there are many other fruit sugars that are used for chemical peeling. 

The key is to find an acid with a low enough ph to disrupt the chemical bonds between the cells and help the exfoliation process. Remember that the story goes that the beautiful Cleopatra used milk and honey on her skin to enhance its beauty (chemical peeling effects) long before Obagi and Neo Strata were ever invented.