Texas has now invited a total of seven to camp.
McClung, 29, didn't pitch last season after being released by the Marlins at the end of March. He went 3-3 with a 4.94 ERA in 41 games with the Brewers in 2009.
The 32-year-old Chavez was in the Rangers organization all of last season but played in only eight Minor League games as he worked his way back from a July 2009 operation on his right knee. He's playing the outfield in the Venezuelan Winter League.
Barden, 29, hit just .179 in 35 games with the Marlins, but he hit .353 at Triple-A. He was a National League Rookie of the Month with the Cardinals in 2009.
Catcher Kevin Cash, outfielder Doug Deeds, infielder Esteban German and right-hander Ryan Tucker have also received Spring Training invites.