Chatwood, 24, made four starts for the Rockies this season, going 1-0 with a 4.50 ERA. He opened the season on the DL with a strained left hamstring.
Chatwood started 20 games last season, going 8-5 with a 3.15 ERA.
Bettis, 24, began the season on the Rockies' Opening Day roster for the first time in his career before being optioned to Triple-A on April 25, where he made one scoreless appearance. He went 0-1 with a 7.15 ERA in 11 appearances during his first stint with the Rockies.