Only front headlamps and rear reflectors are legally necessary. However, taking the extra step of equipping both the front and rear of a bicycle with lights is an excellent idea. There is some debate, however, regarding the best and safest way to illuminate the bicycle rear: Should the rear light blink or remain steady?
The debate arises from something dubbed the "moth effect." Studies considering when emergency vehicles should and should not utilize flashing lights at a crash scene have sometimes demonstrated this effect. Like a moth to a flickering flame, a human being behind the wheel will be attracted to a light blinking in the darkness. The implication is that blinking lights on vehicles, and on the back of bicycles, may be more dangerous than steady lights. Rather than alerting and repelling the motorist, a flashing light may actually draw the approaching vehicle to the light's source causing a collision. Apparently, steady lights do not have such an effect. There is little science, however, that supports the existence of this supposed effect. According to James D. Wells Jr., who conducted a comprehensive 2004 study of the moth effect, "There are no known studies that have not been disproven that substantiate the actual existence of this effect in real world driving." Furthermore, even if there is some evidence for the moth effect in the emergency vehicle context, there are no studies I'm aware of considering its application to bicycles, which generally do not emit nearly as much light as say an ambulance with all lights a-blazin'.
In a dense urban atmosphere bicycles at night at competing to be seen with a lot of illuminated objects, i.e. cars, street lights, flashing pawn broker signs, etc. Moreover, bikes are small in comparison to other vehicles on the road and bike lights can offer relatively little candle power compared to these other illuminated sources. It seems that using a flashing light would help the bicyclist been seen best in the urban road discotheque. The bicyclist should, of course, make up his or her own mind on the subject. Either option is perfectly legal in Illinois. I recommend reading an excellent treatment of the moth effect by human factors expert, Marc Green, complete with study references.