Chytil played for PSG Zlín of the Czech Extraliga during the 2016–17 season. He recorded four goals and four assists in 38 games, which was the second highest total of games played, goals, assists and points among all players under age 18 in the league. He also played two games for Zlín's junior affiliate.[2] A top prospect for the 2017 NHL entry draft, he was selected 21st overall by the New York Rangers. Shortly after the NHL Draft, Chytil was selected seventh overall in the CHL Import Draft by the North Bay Battalion.[3] On 14 July 2017, Chytil signed a three-year, entry-level contract with the New York Rangers.[4]
After participating in the Rangers' training camp, Chytil impressed and was selected by the local media with the Lars-Erik Sjöberg Award as top rookie in camp.[5] He made it through the pre-season to earn a spot on the Rangers opening-night roster for the 2017–18 season.[6] He secured a scoring role playing between Mats Zuccarello and Rick Nash.[6] However, after playing two games at the NHL level, he was reassigned to the Rangers' American Hockey League (AHL) affiliate, the Hartford Wolf Pack.[7] Chytil and fellow first-round pick Lias Andersson were called up by the Rangers on 25 March 2018.[8] Chytil recorded his first NHL goal on 30 March, in a 7–3 loss to the Tampa Bay Lightning.[9] On 29 July 2021, Chytil was re-signed to a two-year contract by the Rangers.[10] On 29 March 2023, he signed a four-year contract extension with the team.[11]
On 2 November 2023, during a 2–1 victory against the Carolina Hurricanes, Chytil suffered the fourth concussion of his career and was placed on injured reserve.[12] On 28 January 2024, he was ruled out for the rest of the 2023–24 regular season after suffering a setback during practice two days earlier.[13][14] Chytil returned to play on 9 May, in game 3 of the second round of the 2024 Stanley Cup playoffs in a 3–2 overtime win over the Carolina Hurricanes.[15]
