NMAC BETWEEN ACR AND CORP-TWIN. SEE AND AVOID CONCEPT.

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ON CLBOUT FROM O'HARE; PASSING THROUGH 10500'; ORD DEP HANDED US OFF TO ZAU. WE CHANGED FREQ AND CHKED IN WITH THE CENTER. HE IMMEDIATELY CALLED TFC AT 12 O'CLOCK; SBND; ALT UNKNOWN. WE PASSED VERY CLOSE BEHIND A LIGHT TWIN WHO WAS SBND AT 11500'. WE WERE NOW ALSO PASSING THROUGH 11500'. WE WERE EBND AT THE TIME. I IMMEDIATELY LEVELED OFF AND STARTED A LEFT TURN TO AVOID COLLISION. A POSSIBLE CONTRIBUTING FACTOR AT THE TIME IS THAT THE ARTS III RADAR SYS WAS INOP AT O'HARE. WE WERE SQUAWKING A NONDISCRETE CODE PRIOR TO THE HDOF. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: RPTR SAYS HE MENTIONED NMAC TO CENTER CTLR; BUT EVIDENTLY DID NOT MAKE IT CLEAR THAT HE WANTED TO FILE A FORMAL NMAC RPT; AND NO FAA PERSONNEL MET HIM AT DEST TO TAKE RPT. SAYS HE COULD EASILY READ NUMBERS ON THE OTHER ACFT AND REVISES MISS DISTANCE TO 400' OR LESS. CTLR IN CENTER SAID HE WAS THE TARGET OF ACFT Y AND TRIED TO GET DEP CTLR ONLINE TO GIVE TFC; BUT APPARENTLY DEP CTLR CHANGED ACR TO CENTER FREQ W/O GETTING THAT WARNING. CENTER GAVE TFC ON FIRST RADIO CONTACT; BUT IT WAS TOO LATE AS ACFT WERE ABOUT TO PASS EACH OTHER. SUPPLEMENTAL INFO FROM ACN 91960: THOUGHT I WAS GOING TO DIE--ALL OVER IN 4 SECS. SAW VERT STABILIZER FROM 50'. OUR HDG WAS 150 DEGS. ACR X HDG WAS 090 DEGS PROX. HE WAS CLBING. CHKED TRANSPONDER BEFORE AND AFTER FLT. EITHER CTLR BLIND OR ACR X CAPT DID NOT WORRY ABOUT DYING. WE NEED TO AUTOMATE THE SYS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: THERE WERE 2 PLTS ABOARD. RPTR HAS ATP RATING. CLOSEST POINT ACFT WERE ABOUT 50' APART. RPTR COULD CLEARLY SEE FACIAL FEATURES OF ACR PIC. NOT IN RADIO CONTACT WITH ANY ATC FAC. HAD TRANSPONDER WITH MODE C OPERATING. LEVEL AT 11500'; WHICH IS CORRECT ALT FOR DIRECTION OF FLT. DID NOT REPORT NMAC TO ANY FAA FAC.