In the City of Chicago, how many unpaid parking tickets does it take
to get booted, and how long must they go unpaid before the car is
booted?

From the City of Chicago website:
  
"Vehicles become boot eligible when a registered owner accrues three
(3) or more unpaid final determinations of parking and compliance
violation liability. If the debt is not paid within 24 hours of
booting, the vehicle is subsequently towed."
  
Booted Vehicle Information
http://egov.cityofchicago.org/city/webportal/portalContentItemAction.do?contentOID=536910186&contenTypeName=COC_EDITORIAL&topChannelName=Dept&blockName=Revenue%2FBoot+%26+Tow+Information%2FI+Want+To&context=dept&channelId=0&programId=0&entityName=Revenue&deptMainCategoryOID=-536889525