1) Bret Saberhagen (Chicago Heights) - 3.34 ERA (126 ERA+) in 2,562.2 innings (1984-2001), with 1,715 strikeouts. 3-time All-Star won the American League Cy Young Award in 1985 and 1989 and is also the last pitcher to throw a postseason Maddux.
2) Charlie Leibrandt (Chicago) - 3.71 ERA (108 ERA+) in 2,308 innings (1979-1993), with 1,121 strikeouts. One of the best pitchers of the expansion era (1961 on) never named to an All-Star team. He and Saberhagen were teammates from 1984-1989, giving those Royals a strong Chicago flavor.
3) Cy Falkenberg (Chicago) - 2.68 ERA (106 ERA+) in 2,275 innings (1903-1917), with 1,164 strikeouts. His best season was probably 1914, when he led the newly formed Federal League in starts (43), innings (377.1), and strikeouts (236) while pitching for the Indianapolis Hoosiers. (Learn more from his SABR biography)
4) Jim O'Toole (Chicago) - 3.57 ERA (106 ERA+) in 1,615.1 innings (1958-1967), with 1,039 strikeouts. Spent most of his career with the Cincinnati Reds and ranks 10th in franchise history in strikeouts. Finished 10th in National League MVP voting in 1961 and started the 1963 All-Star Game. (Learn more from his SABR biography)
5) Johnny Rigney (Oak Park) - 3.59 ERA (122 ERA+) in 1,186.1 innings (1937-1947). White Sox hurler was one of the ten best pitchers in baseball from 1938 to 1941, before missing almost four full seasons due to Naval service in World War II. Would likely rank 2nd or 3rd if he'd played those years.
RP) Jason Frasor (Chicago) - 3.67 ERA (120 ERA+) in 571.1 innings (2004-2013), with 547 strikeouts. Spent nine years as a member of the Blue Jays, but was with the Rangers in 2013 and had the second-best season of his career.
C) Tom Haller (Lockport) - .257/.340/.414 (114 OPS+) in 4,520 PA (1961-1971). In addition to being a strong defender, Haller hit 134 home runs in an era mostly dominated by pitching. He was named an All-Star 3 times and hit a HR off Whitey Ford in the 1962 World Series. (Learn more from his SABR biography)
1B) Phil Cavarretta (Chicago) - .293/.372/.416 (118 OPS+) in 7,701 PA (1934-1955). Spent his entire career in Chicago, 20 seasons with the Cubs, 2 with the White Sox. A 3-time All Star, he also won the 1945 National League MVP Award and received votes in six other seasons.
2B) Marty McManus (Chicago) - .289/.357/.430 (102 OPS+) in 7,565 PA (1920-1934). He received mention in the MVP balloting four times, and batted better than .300 four times as well, in addition to leading the American League in doubles in 1925 and in stolen bases in 1930. (Learn more from his SABR biography)
3B) Freddie Lindstrom (Chicago) - .311/.351/.449 (110 OPS+) in 6,108 PA (1924-1936). In 1924, at age 18, he became the youngest ever to play in the World Series (a record he still holds). In 1928 he hit .358 and finished a close 2nd in the NL MVP balloting. Inducted into the Hall of Fame in 1976. (Learn more from his SABR biography)
SS) Lou Boudreau (Harvey) - .295/.380/.415 (120 OPS+) in 7,024 PA (1938-1952). A 7-time All Star, Boudreau was a player/manager for much of his career and in 1948 he became the only man ever to win the MVP and manage the World Series winner in the same year. Inducted into the Hall of Fame in 1970. (Learn more from his SABR biography)
LF) Rickey Henderson (Chicago) - .279/.401/.419 (127 OPS+) in 13,346 PA (1979-2003). He led the league in stolen bases 12 times, including 1998, when he became the oldest player ever to do it (at age 39). He is the all-time leader in steals (1,406) and runs scored (2,295), a 10-time All Star, and the 1990 AL MVP. Put shortly, Henderson is one of the 25 greatest players in baseball history.
CF) Kirby Puckett (Chicago) - .318/.360/.477 (124 OPS+) in 7,831 PA (1984-1995). A 10-time All Star who finished in the top ten in AL MVP voting 7 times, led the AL in hits 4 times, and won the 1989 batting title. His career was ended early by glaucoma, at a time when his offense hadn't fallen off a bit, likely costing him at least another 500 hits. Inducted into the Hall of Fame in 2001. (Learn more from his SABR biography)
RF) Jesse Barfield (Joliet) - .256/.335/.466 (117 OPS+) in 5,394 PA (1981-1992). In 1986 he hit 40 home runs, won a Gold Glove, and may have been the AL's best player. Hit 241 home runs and was one of the greatest defensive right fielders in history, perhaps behind only Roberto Clemente.
Top Ten Overall
1) Rickey Henderson (Chicago)
2) Lou Boudreau (Harvey)
3) Bret Saberhagen (Chicago Heights)
4) Kirby Puckett (Chicago)
5) Fred Lynn (Chicago)
6) Wally Berger (Chicago)
7) Jesse Barfield (Joliet)
8) Dick Bartell (Chicago)
9) Lonnie Smith (Chicago)
10) Herman Long (Chicago)
Top Five Active
1) Curtis Granderson (Blue Island)
2) Jason Kipnis (Northbrook)
3) Peter Bourjos (Park Ridge)
4) Jason Frasor (Chicago)
5) Tom Gorzelanny (Evergreen Park)
Granderson is knocking on the door of the top ten overall, one more good season would probably land him at #9, and two or three more good years could get him to #6, but given that he'll turn 33 before Opening Day, it's unlikely he does enough over the rest of his career to crack the top five or take over as the team's center fielder. Kipnis has a ways to go, but still only 26 and with 2B being a relative weak spot on the team, he could find his way into the lineup in another four or five years.