Chaisson was chosen to wear the No. 18 Jersey by the Tigers' coaching staff going into his redshirt sophomore season. He finished the season with 60 tackles and led the team with 6.5 sacks, 13.5 tackles for loss, and six quarterback hurries along with two passes broken up and a forced fumble and was named first team All-SEC. Chaisson was named the Defensive MVP of the 2019 Peach Bowl after a six-tackle, two-sack performance against Oklahoma. Chaisson had two tackles in LSU's 42–25 win over Clemson in the 2020 National Championship Game. On January 17, 2020, Chaisson announced that he would forgo his remaining two years of eligibility and enter the 2020 NFL Draft.
Chaisson was selected with the 20th pick in the 2020 NFL draft by the Jacksonville Jaguars. The Jaguars originally acquired the selection in an October 2019 trade with the Los Angeles Rams that sent cornerback Jalen Ramsey to the Rams.
Chaisson made his NFL debut on September 13, 2020 in the season opener against the Indianapolis Colts, making two tackles. In the following week's game against the Tennessee Titans, Chaisson recorded his first career sack on Ryan Tannehill during the 33–30 loss.