To allow people to struggle with this a bit, don't answer any of the options for a day or so. Depending on how much fun you guys have, there are a few other players in the historical legend.
I played college ball in Ohio.
In my first MLB season, I went hitless in over 30 at bats.
I was a fourth-round draft pick.
I played six years in Chicago.
I was three over .500 with the Cubs.
My top at-bat season was with the Cubs.
I was a 10th-round pick of a team on the East Coast.
My dad won a World Series ring.
Mainly, I was a center fielder.
I was in the post -season twice, though not as a Cub.
The team that signed me was the last MLB team I played for.
The Cubs acquired me in a very successful trade.
My best WAR season was as a Cub.
I was born in Tennessee.
I was dealt in a package deal for a player who still holds a HBP record.
The Cubs drafted me in a late round.
I won a World Series Ring.
I was traded late in my career for a player nicknamed for a musical style.
A hockey player is generally considered the most popular athlete with my last name, though he pronounces it differently than I do.
My entire MLB career was in the 1970's.
I attended Northwestern University.
My entire big league career was with the Cubs.
All of my MLB triples occurred in one season.
I player in two different decades, leaving MLB before the draft started.
I attended Morton High School in the Chicago suburbs.
I was born in Cuba.
Cleveland originally signed me.
As a Cub, I had double-digit saves in successive years.
In my only MLB decision as a starter, Gary Carter homered off of me.
I attended Edison High in Miami.
I was attended college in Illinois.
While my name was John, you don't know me by that name.
I played against the Cubs in the post-season one year.
In my two seasons as a Cub, I homered four times.
My forte was pinch hitting.
I was born in an NFL city.
Five of my six career at bats were as a Cubs member.
I played college baseball in the ACC.
I have half as many career wins as losses.
I was a Sixth Round Pick by an Eastern Division club.
I attended University of Puget Sound.
I was a utility infielder.
The Cardinals drafted and signed me.
The only player I was traded for was also traded for a Cubs Hall of Fame pitcher with a retired number.
I played with the Cubs for five seasons.
I played in at least one World Series for the Cubs.
I won at least twenty games in three different seasons.
The Cubs traded me, then later bought me back.
I was buried in Arkansas, the state I was also born in.
Hall of Famer Chick Hafey homered in my MLB debut, though not off of me.