PA28 HAS CLOSE ENCOUNTER WITH B737 NEAR GARY; IN.

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I DECIDED AS WE GOT CLOSE TO GARY; IN; TO GO UP THE LAKE FRONT TO GET OUT OF THE HEADWINDS AS I FLEW TO 10C. WE TURNED TO THE NW ABOUT 10 NM SE OF GYY AND STARTED OUR DSCNT FROM 6500 FT TO 3500 FT AS WE WENT OVER GARY AND THEN PAST GARY TO 2500 FT TO AVOID THE CHICAGO CLASS B AIRSPACE. NORMALLY; THE BIG IRON COMES INTO ORD CLASS B AIRSPACE AT ABOUT 7000-8000 FT MSL; BUT AS WE PASSED THROUGH 5200 FT MSL; 2 NM S OF GARY; SOMETHING BIG PASSED RIGHT UNDERNEATH ME ONLY ABOUT 500 FT LOWER. IT WAS A B737. HE CAME FROM MY 5 O'CLOCK POS; THAT IS IN MY BLIND SPOT; BUT I DID NOT SEE HIM UNTIL HE HAD PASSED UNDERNEATH ME AND WAS AT MY 11 O'CLOCK POS. HE MUST HAVE SEEN ME ON TCAS AND DOVE BELOW ME TO AVOID HITTING US. I TOLD MY PAX TO TAKE A LOOK BACK IN THAT DIRECTION IN CASE ORD WAS LINING UP APCHS THAT WAY AND THERE WERE MORE PLANES. FORTUNATELY; THERE WERE NONE. I HAD JUST SET MY ALTIMETER TO GARY'S SETTING FROM THEIR ATIS AND DOUBLECHKED MY ALT. I RECHKED IT AND IT WAS SET CORRECTLY. I WAS NOT INSIDE THE CLASS B AIRSPACE. I HAD BEEN ON FLT FOLLOWING WHEN I WAS IN SOUTH BEND'S AIRSPACE; BUT THEY HAD CANCELED EARLIER WHEN I LEFT AND ENTERED CHICAGO'S AIRSPACE. NORMALLY; I DO NOT EVEN TRY TO GET FLT FOLLOWING AROUND ORD AND IT IS RARE THAT THE TRACON WILL GIVE IT TO YOU. THEY SIMPLY ARE TOO BUSY.