C90 controller described a deviation event when a departure aircraft was sent to the wrong frequency an entered another sector without coordination/hand off; reporter listed other distracting duties as causal factors.

Narrative

I was working the South and West position while O'Hare was on West Flow. Aircraft X checked on and was RADAR contacted. I then climbed the aircraft to 13000 going west bound. Out of about 11000 I shipped Aircraft X to the EON frequency 120.12 instead of to Malta frequency of 127.07. I only learned this after the tapes were reviewed. What happens after I am not sure. The next call I got was Malta calling asking me to ship Aircraft X. I said I did; but tried him again. He was not on my frequency; but he was climbing out of 17000. I called Malta back and informed him I did not have the aircraft. Recommendation; I had a law enforcement aircraft that we were trying to accommodate and I probably should have kept that aircraft a little higher. Having the law enforcement aircraft where it was added to my work load which may have led to me shipping the aircraft to the wrong center sector because I was busy.