Witnesses tell police a group of cyclists went through a stop light, and the driver of an SUV swerved to avoid hitting one of them but hit another.
The victim, 29-year-old Matthew Mager, was taken to the hospital, where he died.
The executive director of the Chicagoland Bicycle Federation warns people should not rely only on traffic laws to stay safe.
"You should always assume that the traffic light is not the final answer, and you should still be looking out for other people making mistakes before you travel through an intersection," said the Chicagoland Bicycle Federation's Rob Sadowsky.
Mayor Daley has introduced a new ordinance to city council to reduce accidents involving bicycles and vehicles.