B737 FLT CREW WITH ZAU AT 7000 FT EXPERIENCED NMAC WITH UNRPTED SAILPLANE DURING ARR TO MDW.

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I WAS ON THE MOTIF ARR TO MDW TALKING TO ZAU. I CANNOT RECALL THE FREQ; BUT THE LAST ONE BEFORE HDOF TO APCH. WE WERE ORIGINALLY CLRED TO CROSS 5 MI S OF JOT AT 6000 FT AND WERE THEN CLRED TO CROSS 10 MI S OF JOT AT 7000 FT; WHICH WE COMPLIED. FLT CONDITIONS WERE CLR OF CLOUDS AND HAZY WITH FLT VISIBILITY AROUND 5 MI. WE WERE LEVEL AT 7000 FT INDICATING 250 KTS WITH THE FO FLYING. I WAS DOING MY NORMAL SCAN FOR TFC WHEN JUST AHEAD; APPROX 11 O'CLOCK POS; A SAILPLANE APPEARED STRAIGHT-ON IN A STEEP R BANK. IT WENT PAST MY SIDE WINDOW STILL IN THE BANK; BUT VERY CLOSE; MAYBE 200 FT LEFT AND LESS THAN 50 FT ABOVE. THIS ALL HAPPENED IN AN INSTANT; BUT I ACTUALLY SAW THE PLT IN HIS SEAT. THE SAILPLANE WAS A T-TAIL SINGLE SEAT VERSION. MY FO ALSO SAW THE ACFT FOR AN INSTANT AFTER HE MUST HAVE HEARD ME SAY AN '&^%$#.' THERE WAS ABSOLUTELY NO TIME FOR AN EVASIVE MANEUVER. THE ACFT APPEARED OUT OF NOWHERE AND ITS CROSS SECTION STRAIGHT-ON IN HAZY CONDITIONS MADE IT NEARLY IMPOSSIBLE TO SEE. I CALLED THE CTR AND SAID I HAD A CLOSE CALL WITH A SAILPLANE AND WAS ASKED HOW CLOSE. I SAID LESS THAN 500 FT; AND HE ACKNOWLEDGED SAYING THAT NO ACFT WAS BEING PAINTED NEAR ME. I WAS THEN HANDED OVER TO CHICAGO APCH CTL AND ALSO TOLD HIM ABOUT THE SAILPLANE ACTIVITY ON THE ARR; AND HE SAID HE WAS GETTING A HIT EVERY ONCE IN A WHILE IN THAT AREA. I BELIEVE THAT IF WE WERE 100 FT LEFT AND A FEW FT HIGHER; A COLLISION WOULD HAVE OCCURRED. AS A CREW; WE WERE ACTIVELY SCANNING AND PREPARING FOR 'NORMAL' VECTORS TO THE APCH. I SAW NO FAULT IN ATC WHATSOEVER. I WOULD LIKE TO KNOW WHY SAILPLANES ARE ALLOWED TO FLY ON A KNOWN ARR RTE TO ONE OF THE BUSIEST AIRSPACES IN THE COUNTRY; ESPECIALLY WITHOUT A XPONDER. I HAVE WRACKED MY BRAIN TRYING TO THINK OF WHAT I COULD HAVE DONE DIFFERENTLY; BUT FIND NOTHING. WE WERE A STERILE COCKPIT WITH ALL ACFT LIGHTS. I JUST DID NOT SEE THE ACFT COMING; AND ANY REACTION WOULD HAVE BEEN TOO LATE. THE GLIDERS HAVE EVERY RIGHT TO BE FLYING; BUT MAYBE A CHANGE IN THE ARR RTE AWAY FROM GLIDER FIELDS OR AN ALT CAP FOR THEM IN THAT AREA SHOULD BE LOOKED AT. ALSO; TRAINING TO THE GLIDER PLTS IN THE AREA OUGHT TO BE GIVEN; OUTLINING THE HIGH DENSITY ARR RTES TO THE CHICAGO AREA. IT WAS A CHILLING EVENT TO MY FO AND ME. IT WAS A VERY CLOSE CALL.