A 6-foot-2 right-handed hitter, Cholowsky was a Golden Spikes finalist at UCLA and had a 1.088 OPS with 21 homers and 60 RBIs in his junior season.
Tampa Bay picks second and Minnesota is third. San Francisco is fourth and Pittsburgh fifth. Kansas City, Baltimore, the Athletics, Atlanta and Colorado round out the top 10.
The White Sox had the top selection for the first time since taking Harold Baines in 1977.
The White Sox got the No. 1 pick after they lost 102 games last season and won the draft lottery and have pegged Cholowsky as a future star that can help them win their first World Series title since 2005.
Meanwhile, the Chicago Cubs are set to pick 23rd in the first round.
ABC7 Chicago contributed to this report.
The video in the player above is from a previous report.