Chaffee, an undrafted forward, found a home with the Tampa Bay Lightning when he signed a one-year, two-way contract worth $775,000 at the NHL level July 1, 2023. The native of Grand Rapids, Michigan, had 133 hits in 66 games of the 2024-25 season, third-most on the Lightning and second among forwards behind Zemgus Girgensons (174).

Chaffee signed his entry-level contract with the Minnesota Wild on March 24, 2020, following his junior season at the University of Massachusetts. He ended his NCAA career with 95 points (47 goals, 48 assists) in 108 games, including 29 points (16 goals, 13 assists) while a junior and Minutemen co-captain. He was tied for first in power-play points (nine), second in goals, power-play goals (three), game-winning goals (three) and shots on goal (101).

Chaffee was named to the Hockey East All-Academic Team twice (2017, '19) and as a sophomore was honored as a New England All-Star, Hockey East First Team All-Star, Hockey East scoring champion and CCM/AHCA First Team All-American. He won the Herb Gallagher Award given to New England's best forward.

Chaffee played two seasons for Bloomington and Fargo in the United States Hockey League. He made his NHL debut with the Wild on April 19, 2022, and skated in the Stanley Cup Playoffs with the Lightning in 2024 and '25.