The Cubs claimed Orze off waivers from the Twins on Monday.
Orze made 36 appearances for the Twins this season, collecting a 5.66 ERA and 36:21 K:BB over 41.1 innings of work. The 29-year-old is out of minor-league options, so he would have to be exposed to waivers again if the Cubs try to send him to the minors.