Chavez was originally drafted in the 39th round out of high school by the Chicago Cubs, but opted to attend college instead. Chavez was later drafted by the Texas Rangers in the 2002 Major League Baseball Draft out of Riverside Community College. In 2006 Chavez was promoted to Triple-A Oklahoma where he pitched one game before being traded.
Pittsburgh Pirates
The Rangers traded Chavez to the Pittsburgh Pirates for Kip Wells on July 31, 2006. He was assigned to the Triple-A Indianapolis Indians where he pitched the rest of the season and all of 2007. Chavez appeared in 51 games for the Indians in 2007, pitching to a 3.80 earned run average, and was promoted to the majors on August 27, making his debut the same day. He had a 4.48 ERA in 82 innings pitched for the Pirates from 2008–2009.
Atlanta Braves
The Pirates traded Chavez on November 3, 2009, to the Tampa Bay Rays in exchange for second baseman Akinori Iwamura. On December 10, he was traded again, to the Atlanta Braves for Rafael Soriano. He had a 5.89 ERA in 36 innings pitched for the Braves in 2010.
Kansas City Royals
On July 31, 2010, Chavez was traded to the Kansas City Royals along with Gregor Blanco and Tim Collins for Rick Ankiel and Kyle Farnsworth. The Royals designated him for assignment on October 11, 2011. He had a 6.95 ERA in 33 innings pitched for the Royals from 2010–2011.
Toronto Blue Jays
On October 21, 2011, he was claimed off waivers by the Toronto Blue Jays. He was designated for assignment on December 12 but cleared waivers and was outrighted to Triple-A. On May 27, 2012, Chavez was called up from the Triple-A Las Vegas 51s. He was 6–2 with a 3.72 ERA in 10 games with Las Vegas. He was recalled on August 4. On August 5, however, he was sent back down to make room for the promotion of Chad Jenkins from the New Hampshire Fisher Cats.
Oakland Athletics
Chavez was traded to the Oakland Athletics on August 24, 2012, in exchange for cash considerations. Chavez began the 2013 season with the Triple-A Sacramento River Cats. He was recalled by Oakland on April 20, and sent back to Sacramento on April 29. He was recalled again on May 10. On June 13, Chavez pitched 5 shutout innings of relief in an 18-inning game against the New York Yankees, earning the win. On July 31, Chavez pitched against the Blue Jaysfor the first time since being traded to Oakland and took the loss, yielding 3 runs in the 10th inning. Chavez was added to Oakland's starting rotation to open the 2014 season, due to the spring injuries of Jarrod Parker and A.J. Griffin. He set career highs in starts and innings pitched, and finished with an 8–8 record with a 3.45 ERA. On January 12, 2015, Chavez and the Athletics agreed to a one-year deal worth $2.15 million, avoiding arbitration. Chavez was placed in the bullpen to start the season. On April 23, he was moved to the rotation and ended up making 26 starts for Oakland, a career high, pitching to a 7–15 record and a 4.18 ERA. His season ended in mid-September when he was diagnosed with a non-displaced fracture in his ribs.
Second stint with Toronto
On November 20, 2015, the Athletics traded Chavez to the Blue Jays for Liam Hendriks. He and the Blue Jays did not come to an agreement before the salary arbitration deadline on January 15, 2016. Chavez was seeking $4 million, while the Blue Jays countered at $3.6 million. On February 6, it was announced that Chavez had won his arbitration case. Chavez entered spring training in competition for the fifth starter role with Aaron Sanchez, Drew Hutchison, and Gavin Floyd. On March 28, it was announced that Sanchez would be the team's fifth starter, and Chavez would begin the season in the bullpen. Chavez pitched to a 1–2 record, 4.57 ERA, and 42 strikeouts in 41 innings before being traded.
Los Angeles Dodgers
On August 1, 2016, the Blue Jays traded Chavez to the Los Angeles Dodgers for Mike Bolsinger. He appeared in 23 games for the Dodgers with a 4.21 ERA.
Los Angeles Angels
On November 11, 2016, Chavez signed a one-year, $5.75 million contract with the Los Angeles Angels. Chavez was chosen to start in the Angels rotation at the beginning of the season due to the bevy of injuries. Chavez made 21 starts, going 5-9 with a 5.24 ERA before being put in the bullpen after the All Star Break. Chavez finished the season 7-11 in 38 games, 21 starts.
Texas Rangers
On February 23, 2018, Chavez signed a one-year contract with the Texas Rangers.
Chicago Cubs
On July 19, 2018, Chavez was acquired by the Chicago Cubs for minor league pitcher Tyler Thomas. Chavez posted an impressive 1.15 ERA in 32 appearances with the Cubs.
Second stint with Texas
In November 2018, Chavez signed a 2-year contract to return to the Texas Rangers. Chavez was placed on the injured list on August 13 with elbow inflammation, which stemmed from a bone spur. He finished the 2019 season going 3–5 with a 4.85 ERA in 78 innings. Chavez underwent surgery to remove loose bodies from his elbow on September 9.
