Kershaw makes his first start of spring training on the mound, one of six scheduled spring outings before his planned start on opening day April 6 at Dodger Stadium against the Padres.
Puig didn't play in Wednesday's spring opener, with Friday's split squad prompting manager Don Mattingly to stagger days off for many of his regulars. Puig will start in right field Thursday, while A.J. Ellis catches Kershaw, Scott Van Slyke plays first base and Justin Turner starts at third base.
Joc Pederson, who was 2-for-2 with a double as the designated hitter in Wednesday's opener, will start in center field on Thursday.
Corey Seager saw time at DH on Wednesday and will play shortstop in reserve on Thursday. Mattingly in the early going said he likes his starters to play roughly four innings or two plate appearances.
In other position-switching moves, Enrique Hernandez starts at second base Thursday after playing shortstop on Wednesday, Darnell Sweeney goes from center field to second base, Chris Heisey goes from right field to designated hitter, Alex Guerrero goes from third base to DH, and O`Koyea Dickson will play left field after playing first base on Wednesday.
Following Kershaw on the mound for the Dodgers will be Joe Wieland, Chris Hatcher, Brandon League, Daniel Coulombe and Ryan Buchter.
John Danks starts for the White Sox.
Other Dodgers scheduled to suit up Thursday include catchers Chris O`Brien and Shawn Zarraga, infielder Erisbel Arruebarrena, as well as James Baldwin, Joey Curletta and Luis Mateo from the minor league side.