NUMEROUS TCASII TA RA WITH INTRUDER HELI ACFT BELOW 1200 FT AGL AND NMAC DISTANCE TO B757 ACFT AT ORD.

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ON FINAL APCH RWY 27L VISUAL AT ORD. AT APPROX 1200 FT AGL; TCASII TA ALERTED TO TFC AT 1 O'CLOCK POS LESS THAN 2 MI; 600 FT BELOW AND CLBING. NO TFC SEEN VISUALLY. ABOUT 5-8 SECONDS LATER AND AFTER A SECOND TCASII TA WITH NO VISUAL SIGHTING; TCASII RA ALERTED WITH CLB INSTRUCTIONS. CAPT INITIATED CLBING L TURN FROM LESS THAN 1000 FT AGL. AT THE SAME TIME THE FO SPOTTED A HELI AT 1 O'CLOCK POS LESS THAN 1 MI. WE WERE AT HELI'S 7 O'CLOCK RELATIVE POS AND CLOSING. THE FOLLOWING HAPPENED NEARLY SIMULTANEOUS: CAPT AND FO OBSERVED HELI IN CLBING L TURN INTO OUR LINE OF FLT. CAPT CONTINUED L CLBING TURN TO AVOID CONFLICT. ORD TWR RPTED THE HELI AS TFC. HELI OBSERVED SHALLOWING TURN RADIUS THEREBY DECREASING DISTANCE BTWN ACFT. ORD TWR RPTED HELI HAS US 'INSIGHT.' CAPT CONTINUED FURTHER L CLBING DEV TO AVOID HELI DUE TO HELI'S DECREASED TURN RADIUS. ONCE CLR OF HELI; CAPT CONTINUED APCH TO AN OTHERWISE UNEVENTFUL LNDG. ESTIMATED CPA LESS THAN 500 FT AT CO-ALT. RECOMMENDATION: DO NOT PERMIT HELI OR ANY OTHER ACFT OPS BTWN PARALLEL APCH CORRIDORS AT THE SAME ALTS AS ACFT IS ON APCH. MANY PAX VERY CONCERNED ABOUT THEIR SAFETY.