Streveler played two years with the South Dakota Coyotes at the University of South Dakota. Streveler threw for 6,081 yards and 54 touchdowns, earning the MVFC Offensive Player of the Year award in 2017. He was a runner-up for the Walter Payton award. He spent three years at Minnesota before going to South Dakota.
On May 4, 2018, Streveler signed with the Winnipeg Blue Bombers of the Canadian Football League after going undrafted in the 2018 NFL Draft. Expected to compete with Blue Bombers' quarterbacks Matt Nichols, Darian Durant and Alex Ross in training camp, to-be backup quarterback Darian Durant retired before the start of training camp. The Blue Bombers signed quarterback Bryan Bennett to compete with Streveler and Ross for backup behind Nichols. On June 1, 2018, Streveler played in his first preseason game with the Blue Bombers, going 10 for 10 with 140 yards and an 80-yard touchdown pass. On June 6, Nichols suffered an injury in practice that would later sideline him for four to six weeks to open the 2018 season. Instead of signing a veteran quarterback to lead the team, the Blue Bombers elected to start Streveler to open the season. Streveler became the first quarterback to start a CFL game coming out of college since 1994, when future Hall of Famer Anthony Calvillo started for the Las Vegas Posse. Streveler won his first CFL match in Week 2 when the Bombers defeated the Alouettes 56–10. Streveler started the first three games of the season for the Bombers before starting quarterback Matt Nichols returned from injury. Streveler continued to be utilized as a rusher and rotational passer, and finished the season by completing 86 out of 140 passes for 1,134 yards and 11 touchdowns against 5 interceptions. On the ground, Streveler had 77 carries for 441 yards and 10 more scores.
Chris Streveler began the 2019 season as the backup quarterback to Matt Nichols. Nichols suffered an injury in Week 10 and was placed on the six-game injured reserve list, which promoted Streveler to the starting role. Despite completing only seven passes for 89 yards Streveler was able to lead the Bombers to a win thanks in part to his rushing performance in which he gained 95 yards and scored a touchdown.