Chris Heston graduated from Bayside High School in Palm Bay, Florida. He played college baseball for two years at Seminole Community College. He was drafted by the Minnesota Twins in the 47th round of the 2007 Major League Baseball Draft but did not sign with the team. In 2008 the Washington Nationals drafted Heston in the 29th round, but he again did not sign and attended East Carolina University. He was then drafted a third time, by the San Francisco Giants in the 12th round in 2009, and signed.
Heston made his Major League debut with the San Francisco Giants on September 13, 2014, in the ninth inning against the Los Angeles Dodgers where he pitched a scoreless inning. He eventually appeared in three games, including one start, and pitched five and one-third innings with a 5.06 ERA. The Giants clinched a wild card spot with an 88–74 record and eventually won the 2014 World Series, their third championship in five seasons. Heston did not participate in any postseason activity but received his first championship ring for his regular season contributions.
Heston was slated to start the 2015 season in AAA Sacramento, but was called up on April 7 to replace the injured Matt Cain. He got his first MLB win in his second start for the Giants on April 8, 2015, defeating the Arizona Diamondbacks 5–2 and throwing 6 innings. Heston gave up two runs, neither earned, but had five strikeouts gaining the win. On May 12, 2015, Heston pitched a complete game against the Houston Astros, allowing only two hits and one run, with 10 strikeouts and no walks. Heston was the first Giants rookie to throw a complete game with at least 10 strikeouts since Roger Mason on October 4, 1985, and the first Giants rookie with double-digit strikeouts since Tim Lincecum on July 1, 2007.
On June 9, 2015, Heston no-hit the New York Mets 5–0 at Citi Field, becoming the 22nd rookie pitcher since 1900 to throw a no-hitter in a major-league regular-season game. He struck out 11 and walked none; the only 3 runners to reach base were hit by a pitch. Heston closed his no-hitter with three strikeouts in the 9th inning, a feat last accomplished by Sandy Koufax in his perfect game in 1965 against the Chicago Cubs. He also became the first pitcher to no-hit the Mets in a Mets’ home game since Pittsburgh’s Bob Moose no-hit them at Shea Stadium in 1969. In the same game, Heston logged his first career RBIs with a two-run single. For his efforts, Heston was honored his first career National League Player of the Week Award as well as the key to the city by the mayor of Palm Bay, Florida.
On July 23, 2015, Heston carried a no-hitter into the sixth inning against the San Diego Padres, ultimately allowing only one hit and no runs in 7 1⁄3 innings pitched. The 9–3 victory over the Padres was Heston’s 10th win, making him the first Giants rookie to reach 10 wins since Matt Cain in 2006.