B737 CREW AND AN ACR CL65 HAD LESS THAN LEGAL SEPARATION IN ORD CLASS B AIRSPACE.

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WE RECEIVED THE FOLLOWING CLRNC: FLY 260 DEG HDG; CLRED FOR TKOF RWY 27L. DURING OUR TKOF ROLL; I HEARD THE TWR DIRECT AN ACFT TO GO AROUND. THE RWY THE GAR ACFT WAS ATTEMPTING TO LAND ON WAS NOT MENTIONED. WHILE WE WERE CLBING ON A 260 DEG HDG; THE FO STATED TERSELY 'STOP CLB.' I LOWERED OUR NOSE AND STOPPED CLBING AND ASKED WHAT WAS UP; TO WHICH HE REPLIED 'WE HAVE TFC.' I LOOKED OUT HIS SIDE WINDOW AND SAW THE UNDERSIDE OF AN ACR Y RJ WHICH WAS IN A CLBING TIGHT R TURN AWAY FROM US GOING THROUGH A HDG PARALLEL TO OURS. HE SEEMED JUST SLIGHTLY ABOVE US. AT NO TIME DID WE RECEIVE A TCASII AURAL ALERT. THE ACFT APPEARED TO COME WITHIN 1/2 MI BY THE FO'S ESTIMATION; BUT IT LOOKED CLOSER -- PERHAPS 1/4 MI. WE KEPT VISUAL SEPARATION FROM THE RJ. THE TWR TOLD US TO TURN L 220 DEGS. WE THEN SAW A YELLOW TCASII TARGET WITH AN ALT READOUT OF +400 FT ON OUR NDS THAT CORRELATED TO THE RJS POS. OUR ALT WAS APPROX 1600-2000 FT MSL. GIVEN THE POS OF THE RJ; I PRESUME HE WAS EXECUTING A MISSED APCH TO RWY 14R. OUR ACTIONS TO AVOID CLOSURE BTWN OUR 2 ACFT WERE BASED ON OUR VISUAL SIGHTING OF THE RJ IN THE ABSENCE OF TCASII OR ATC GUIDANCE. SUPPLEMENTAL INFO FROM ACN 539707: I LOOKED UP AND SAW AN RJ AT OUR 2 O'CLOCK POS. HE WAS A YELLOW CIRCLE ON MY TCASII SCREEN AND SHOWING 400 FT ABOVE US. I GUESS THE RANGE WAS ABOUT 1/2 NM; AND THAT WAS THE CLOSEST POINT OF APCH. I CALLED THE TFC AND TOLD THE CAPT TO LEVEL OFF. JUST THEN TWR GAVE US A HARD L TURN TO 200 DEGS. WE WERE TOO LOW FOR THE TCASII TO GIVE US ANY TFC CALLS -- BELOW 1100 FT AGL. I DON'T THINK THEY EVER PICKED US UP VISUALLY. CALLBACK CONVERSATION WITH RPTR ACN 539099 REVEALED THE FOLLOWING INFO: THE CONFLICTING ACFT WAS A CL65. THE RPT WAS INVESTIGATED BY THE ACR SAFETY DEPT. THEIR RPT WAS TURNED OVER TO THE FAA AT ORD. THEY INDICATED CTLR TRAINING WAS BEING CONDUCTED. THEY INDICATED THE B737 SHOULD NEVER HAVE BEEN GIVEN TKOF CLRNC. BOEING HAS SUPPRESSED ALL AURAL TCASII WARNINGS BELOW 1100 FT RADIO ALT. THIS WOULD ACCOUNT FOR THE LACK OF TCASII AURAL WARNING. THE CAPT WAS USING THE ACFT HUD FOR TKOF; SO HE HAD THE OUTSIDE ENVIRONMENT ALREADY IN SIGHT THROUGH THE HUD.