Generally I would say yes.
It's best if you live close to the lakeshore so you can take advantage of the lakefront trail. The trail runs the length of the city, with very few intersections with car traffic. You do have to be mindful of pedestrians on the trail who aren't paying attention, particularly in the summer, but an expansion is in the works that will divide the trail into distinct bike and pedestrian lanes. The trail is even well-maintained and kept clear in the winter (mostly).
Chicago also benefits from many bike lanes, some are event protected and have their own traffic lights.
The local bikeshare program, "Divvy" is reasonably priced at $99 a year with unlimited 30 minute rides, and the stations are numerous and conveniently located. Though I own and prefer using my own bike, I use Divvy for one way trips and commuting to and from work, about a 9 mile ride from my home in the Edgewater neighborhood to my office in the Loop, using the lakefront trail.
Chicago also has all the usual bike-centric social groups (Critical Mass, BFF Bikes, etc), and an innovative volunteer group called Working Bikes that collects and fixes up bikes to send to developing countries.
So I would say it's a good place to be a bicyclist, and I enjoy it.