When Chychrun was 13, he joined the Little Caesars hockey organization in Detroit, Michigan, where he played very well during his major bantam season.

He subsequently missed eight weeks, including the 2014 World Under-17 Hockey Challenge, before returning to the lineup on December 19.

[7] As a member of the Sting, Chychrun attended Northern Collegiate Institute and Vocational School and was recognized as the West Division Academic Player of the Month for November 2014.

[17] He earned these honours despite missing the final 26 games of the regular season and the OHL 2015 playoffs because of an upper-body injury.

[18] By October 21, Chychrun had registered one goal, five assists, and a plus-6 rating through his first 10 games and was selected to participate in the 2015 CHL Canada-Russia Series.

[1] On July 30, 2016, Chychrun concluded his OHL career and signed a three-year, NHL entry-level contract with the Coyotes.

[23] Due to his impressive play, Chychrun subsequently became the youngest player in Coyotes history to make his NHL debut with the team at 18 years and 198 days.

[24][25] As a result of his age, Chychrun would not be eligible to play in the American Hockey League (AHL) for the 2016–17 season if the Coyotes wished to move him.

[26] He tallied his first career NHL point, an assist, in his debut game to lift the Coyotes to a 4–3 win over the Philadelphia Flyers.

[31] Chychrun continued to be made a healthy scratch throughout the season and he sat out four consecutive games in early to mid-February.

[34] Chychrun finished his rookie season tied for second among first-year NHL defencemen with seven goals and seventh for points with 20.

[40] He made his NHL season debut that night, scoring a goal in 22:40 minutes of ice time in a 3–2 loss to the Vegas Golden Knights.

[42] Chychrun underwent surgery to repair his torn ACL in the 2018 off-season but was ruled eligible to play for the 2018–19 season.

[45] Chychrun scored an assist in his return to the lineup on November 21 as the Coyotes fell to the Golden Knights in overtime.

[48][49] He finished the season tying his career high with 20 points through 53 games[50] as the Coyotes failed to qualify for the 2019 Stanley Cup playoffs.

[54] By February 11, Chychrun had maintained a career-best four game point streak and tied for fifth on the team in goals scored.

[59] When the season resumed, Chychrun was healthy enough to join the Coyotes for the 2020 Stanley Cup Qualifiers against the Nashville Predators.

[58] Prior to the start of the Qualifiers, Coyotes general manager and president of hockey operations John Chayka quit and was replaced by his assistant, Steve Sullivan.

[64] Chychrun began the season strong, registering four multi-point games by February 22 to rank second in scoring among West Division defencemen with 13 points.

[74] In his first full year with the Senators, Chychrun scored 14 goals and 41 points, matching his career high.

[75] On July 1, 2024, the Senators traded Chychrun to the Washington Capitals in exchange for defenceman Nick Jensen and a third-round pick in the 2026 NHL entry draft.