A Gold Glove winner in 2012, Barney committed just four errors with a .993 fielding percentage last season. But he also batted .208.
The agreement leaves pitcher Jeff Samardzija as the team's only remaining player in arbitration.
Chicago also announced Thursday that its home game against Washington scheduled for Sunday, June 29, has been moved up a day to ease potential congestion with the annual Pride Parade. The Cubs and Nationals will play a day-night doubleheader on June 28.
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