UNAUTHORIZED PENETRATION OF AIRSPACE. PROX OF TCA.

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INBOUND TO CGX I CALLED CHICAGO RADAR 25 DME 265 DEG OF DPA. HE ACKNOWLEDGED AND GAVE ME SQUAWK CODE AND SAID TO STAY CLR OF TCA AND RPT ANY ALT CHANGE TO HIM. AT ABOUT 5 MI NW OF DUPAGE ARPT (AT 300 MSL) I WAS TOLD TO CONTACT DUPAGE TWR AND AFTER THEY (DPA) RELEASED ME RECONTACT CHICAGO. I CONTACTED DPA TWR. GAVE MY POS AND WAITED FOR THEM TO RELEASE ME BACK TO CHICAGO. AT ABOUT 10 DME ORD; DPA TWR TOLD ME TO FLY A 180 DEG HDG QUICKLY AND RECONTACT CHICAGO. (MY COURSE OF FLT AND UP UNTIL THEN HAD BEEN ABOUT 90 DEG.) I CONTACTED CHICAGO HE SAID HE HAD TOLD ME TO REMAIN CLR OF TCA (AT THIS POINT I WAS 3000 MSL AND FLOOR OF TCA WAS 1900) AND TOLD ME TO GET BELOW 1900 MSL WHICH I DID. HE THEN HANDED ME OFF TO MIDWAY TWR AND I HAD NO MORE CONTACT WITH CHICAGO. IN RETROSPECT MY THOUGHTS WERE THAT I SHOULDN'T CHANGE ALT UNLESS IN CONTACT WITH CHICAGO RADAR AS HE SAID TO RPT ANY ALT CHANGE TO HIM. NEXT TIME I GO TO CHICAGO I WILL ENTER FROM THE SW TO AVOID GOING TO A TWR FREQ DURING ALT CHANGES TO AVOID THE TCA.