Chafin was the 43rd player taken overall, a compensation pick for the loss of free-agent first baseman Adam LaRoche.
After missing all of 2010 following Tommy John surgery, Chafin was 7-1 with a 1.90 ERA and 97 strikeouts this year.
The 20-year-old has an above average fastball that reaches 94 mph and sits at 91-92 with a lot of movement. He also throws a curve and a slider, with the curve being his out pitch.
Chafin, who is listed at 6-foot-2 and 205 pounds, also has a changeup.
The D-backs also took pitchers with their two first-round picks, nabbing UCLA right-hander Trevor Bauer and Oklahoma prep righty Archie Bradley.
"You can never have enough pitching," D-backs general manager Kevin Towers said.