[2] Kilian spent his first professional season in 2019 with the rookie–level Arizona League Giants and Low–A Salem-Keizer Volcanoes and did not allow an earned run over 16 innings.

[4] On July 30, 2021, the San Francisco Giants traded Kilian along with Alexander Canario to the Chicago Cubs in exchange for Kris Bryant.

He won the AFL Championship Game's MVP Award after throwing six perfect innings, retiring all 18 batters he faced.

[8] On June 4, 2022, Kilian was selected to the 40-man roster and promoted to the major leagues for the first time to start against the St. Louis Cardinals.

[9] He made 3 starts for Chicago in his rookie campaign, struggling to an 0-2 record and 10.32 ERA with 9 strikeouts in 11.1 innings pitched.