When Chuck Taylor, who was born in rural southern Indiana in 1901, left home at age 17 to play professional basketball, he was following an unlikely dream. The game of basketball—invented by James Naismith, a YMCA physical fitness instructor in Massachusetts in 1891—was still a minor sport in America. Few competitive leagues existed, and those that did were regional. Most organized teams were subsidized by large manufacturing concerns, such as General Electric or the Firestone Tire and Rubber Co., or …