Chavez, who has a 3-1 record and a 3.51 ERA in 30 relief appearances this season, has struck out 50 batters in 56.1 innings for the Rangers. He is a versatile pitcher, with experience both as a starter and as a reliever, and gives the Cubs insurance in their bullpen, which has been hammered by injuries this season.
Chavez is expected to join the Cubs on Saturday, but a corresponding roster move has not been made to put him on the active roster.
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In exchange, the Cubs sent left-handed pitcher Tyler Thomas to the Rangers. Thomas, who was playing in Single-A, was a seventh round pick of the Cubs in the 2017 MLB Draft, and had a 2.88 ERA in 15 appearances in South Bend this season.
According to the Cubs, their 40-man roster now stands at 39 players.