Chacin, 27, pitched six seasons with the Rockies, posting ERAs under 4.00 in 2010, 2011 and 2013. But last season in Colorado, the right-hander was 1-7 with a 5.40 ERA in 11 starts.
Chacin was in the Indians organization earlier this season, but opted out of his deal after pitching to a 3.21 ERA for Triple-A Columbus.
He was scheduled to start for Triple-A Reno on Saturday night.
Yasmany Tomas was out of the D-backs' starting lineup on Saturday night after leaving Friday's game early with a left elbow contusion. Tomas was hit in the elbow by a James Shields pitch in the first inning, but stayed in the game until after the third. He did pinch-hit in Saturday's game, going 0-for-1.
Tomas' X-rays on Friday were negative and the rookie was optimistic that it would not be a concern moving forward.
"It's just still a little swollen," D-backs manager Chip Hale said.
Tomas has excelled in his first season, leading all National League rookies with a .324 batting average. He also has 18 multi-hit games and set the club's rookie record with 31 hits in May.
Jake Rill is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.