On July 30, 2018, Chivilli signed with the Colorado Rockies as an international free agent.[1] He made his professional debut in 2019 with the Dominican Summer League Rockies. Chivilli did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[2]
Chivilli returned to the DSL Rockies in 2021, recording a 3.49 ERA and 45 strikeouts across 11 games (8 starts).[3] He split the 2022 campaign between the rookie–level Arizona Complex League Rockies and Single–A Fresno Grizzlies. In 32 games out of the bullpen for the two affiliates, Chivilli accumulated a 2.21 ERA with 51 strikeouts across 40+2⁄3 innings pitched.[4]
Chivilli spent 2023 with the High–A Spokane Indians and Double–A Hartford Yard Goats. He made 53 appearances for the two affiliates, compiling a 4–9 record and 5.61 ERA with 68 strikeouts and 17 saves.[5] On November 14, 2023, the Rockies added Chivilli to their 40-man roster to protect him from the Rule 5 draft. He was optioned to Double–A Hartford to begin the 2024 season.[6]
On May 3, 2024, Chivilli was promoted to the major leagues for the first time.[7] He was optioned down to Hartford on May 6 without having appeared for Colorado, becoming a phantom ballplayer.[8] On June 3, Chivilli was once more promoted to the major leagues.[9] This time, he made his MLB debut.[10]