Well it is a difficult question - because most players play for different teams during their career(s). For sure you have Ernie Banks, Ferguson Jenkins, Ryne Sandberg, Billy Williams. Check this link to see who you think are the "real Cubs" http://entertainment.howstuffworks.com/Chicago-cubs-hall-of-fame-members.htm
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Andre Dawson
Ryne Sandburg
Bruce Sutter
Fergie Jenkins
Billy Williams
Ernie Banks
Hack Wilson
Tinkers to Evers to Chance
Cap Anson, Ernie Banks, Billy Williams and of course Tinker, Evans and Chance. Michael Barrett, Mike DiFelice and Paul Bako.
Grover Cleveland Alexander.
Alexander was elected in 1938 and played for the Cubs between 1918-1926.