[3] On July 26, 2021, Palencia, along with Greg Deichmann, was traded to the Chicago Cubs for Andrew Chafin.
In 2022, Palencia played for the High–A South Bend Cubs, making 21 appearances (20 starts) and logging a 3.94 ERA with 98 strikeouts across 75+1⁄3 innings pitched.
In 18 games split between Tennessee and the Triple–A Iowa Cubs, he registered a 6.83 ERA with 36 strikeouts and 2 saves in 29.0 innings pitched.
On July 4, 2023, Palencia was promoted to the major leagues for the first time, winning his debut in extra innings.
[6] In 27 relief outings in his rookie campaign, he logged a 5–3 record and 4.45 ERA with 33 strikeouts across 28+1⁄3 innings pitched.