It’s “Rent The Chicken,” not “Rent-A-Chicken.” Local entrepreneurs Phil and Jenn Tompkins stress the distinction because their South Buffalo Township-based business, Rent The Chicken, in their assessment, is on top of the pecking order of live chicken rental businesses, which includes Michigan-based competitor Rent-A-Chicken.Rent The Chicken continues to add customers after the Tompkins hatched the business five years ago for supplemental income promoting a shared value of the couple: Homesteading — producing yard-to-the-table fresh food.The success of the business illustrates the popularity of backyard hen houses, especially in urban areas. Nearly 4 percent of households surveyed in four major American cities planned to have chickens in the coming years, telltale of the growing acceptance of urban farming, according to a 2013 study by the U.S. Department of Agriculture.