Gaynor, signed by the Bears June 20, 2011, holds the distinction of playing for the Toms River Little League team that captured the Little League World Series championship in 1998. He pitched for four years at Rutgers University, where he won four games as a freshman (4-3 with a 4.82 ERA) and five as a senior (5-3, 5.15 ERA). He signed as a free agent with the Cleveland Indians' organization and spent the 2010 season with Mahoning Valley of the New York-Penn League (Class A), posting 5-2 record with a 4.04 ERA in 16 games, five of which were starts.