C172 PLT WAS CLRED INTO ORD CLASS B BY CGX TWR WITHOUT COORD WITH C90.

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AFTER DEP FROM CGX; CLRNC WAS GIVEN TO CLB TO CRUISE ALT OF 5500 FT MSL. UPON REACHING 5300 FT MSL; I WAS INFORMED THAT I WAS LEAVING CGX AIRSPACE AND SHOULD CONTACT GYY SINCE I WAS GOING TO TURN TO ON COURSE HDG (094 DEGS) FOR HOME BASE (TTF) OVER GYY. I MADE INITIAL CALL-UP TO GYY AND RPTED POS AND ALT OF 5300 FT CLBING TO 5500 FT. GYY APCH ASKED ME IF I HAD BEEN TALKING TO ORD. I INFORMED THEM I HADN'T THEN REALIZED MY MISTAKE. GYY GAVE ME ORD FREQ AND I CONTACTED THEM IMMEDIATELY RPTING POS AND ALT. ORD REQUESTED MY DEST AND INTENTIONS TO WHICH I REPLIED I WAS DSNDING AS FAST AS POSSIBLE TO GET OUT OF CLASS B AIRSPACE. ORD ASKED IF I HAD A CLASS B CHART; I REPLIED I HAD ONLY A SECTIONAL. AFTER APPROX 5 MINS OF ORD CTL; I WAS HANDED OFF TO SBN. OBVIOUSLY I SHOULD HAVE KEPT MYSELF CLR OF CLASS B; AND I AM THE FINAL ONE RESPONSIBLE FOR MY FLT. HOWEVER; MEIGS HANDED ME OFF TO GYY AFTER CLRING ME FOR 5500 FT. THIS WAS A MISTAKE ON MY PART; AND WAS REALIZED AS SOON AS GYY MENTIONED ORD. I IMMEDIATELY BEGAN A DSCNT TO CLR CLASS B AIRSPACE AS I WAS CONTACTING ORD.