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.