Chicago isn't the friendliest city for road biking. Your options are to use the Lakefront path, which isn't safe for high speed bicycling because of joggers, pedestrians, dogs, tourists, and what not, or to use the city streets, which aren't particularly safe due to traffic.
Bike Rental:
You can rent a bike through one of Bike and Roll Chicago's 10 locations - http://www.bikechicago.com/rent-a-bike - they have road bikes and hybrid/comfort/urban bikes.
Bike Stores:
This location in Millennium park offers bike rentals, guided bike and Segway tours, bicycle repair, commuter center. and is open year round.
Location:
239 E. Randolph Street
Chicago,
IL 60601
The Navy pier outpost of Bike and Roll Chicago is open April through October, and offers bike rentals, guided bike tours, bicycle repair, pedicabs.
Location:
600 E. Grand Avenue
Chicago,
IL 60611
At this lakeside location, you can get bike rentals, guided bike tours, quadcycle rentals, and bike share memberships from May to September
Location:
6300 S. Lakeshore Drive
Chicago,
IL 60637
On North Avenue Beach, Bike and Roll offers bike rentals, beach rentals, bicycle repair, beach volleyball.
Location:
1603 N. Lake Shore Drive
Chicago,
IL 60614
The Loop location of Bike and Roll offers Segway Tours (oh boy!) and bike rentals. It's open April to November 15.
Location:
316 N. Wabash Avenue
Chicago,
IL
Rent a bike at this popular swimming beach on Lake Michigan, open Memorial Day to the end of September.
Location:
Oak St at Lake Shore Drive
Chicago,
IL 60611
Rent bikes for the lakeside path and get a quick snack at this seasonal location of Bike and Roll (April-October).
Location:
1300 S. Lake Shore Drive
Chicago,
IL 60605
Rents bikes and quad cycles from Memorial Day to Labor Day for those of you who love the Chicago River!
Location:
200 E. Riverwalk South
Chicago,
IL 60611
Open from Memorial Day to Sept 30 for bike rentals and guided Segway tours
Location:
5200 N. Lake Shore Drive
Chicago,
IL