Flychaser (1887)

“Murphy was again around when wanted, but Glenn was the kingpin of the fly chasers. He not only got everything in reach, but when a ball did go safe he picked up the ball and got it into the diamond with lightning speed.” “One to Nothing. And the Shutout Honor Belongs to Charleston,” Picayune (New Orleans), April 29, 1887, p2

Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1912.  “[Otis Crandall] turned out to be a very good fly chaser.” (Christy Mathewson, Pitching in a Pinch; Peter Morris).