A320; CRUISING AT FL350; EXPERIENCED TCASII RA UNDER ZAU CTL.

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CRUISING AT FL350; APPROX 60 NM E OF MVZ; WE HAD A TCASII TA. WE REDUCED THE RANGE ON THE ND AND OBSERVED A TCASII TARGET ABOUT 10 NM; 900 FT BELOW US AND CLBING. TARGET WAS AT OUR 10 O'CLOCK POS AND HDG TOWARDS US ON A COLLISION COURSE. ALMOST IMMEDIATELY; WE RECEIVED A TCASII RA DIRECTING US TO 'CLB.' PWR WAS ADVANCED TO TOGA; AUTOPLT DISCONNECTED AND WE PITCHED UP UNTIL WE HAD A VERTICAL SPD IN THE 'GREEN' ZONE. CHICAGO ARTCC WAS ADVISED THAT WE WERE RESPONDING TO A TCASII RA WARNING. WE RECEIVED THE 'CLR OF CONFLICT' AT APPROXIMATELY FL365 AND LEVELED THE ACFT AT FL367. ONCE WE WERE SURE WE WERE CLR OF THE TFC; WE RECEIVED CLRNC BACK TO FL350. CHICAGO ARTCC MADE NO EFFORT TO INFORM US OF THE TFC UNTIL WE HAD BEGUN THE RA EVASIVE MANEUVER. AT THAT TIME THE CTLR DIRECTED US TO TURN L 30 DEGS. WE COMPLIED WITH THE TURN BUT CONTINUED TO CLB AS DIRECTED BY THE TCASII. INFO FROM THE CHICAGO ARTCC CTLR WAS NOT FORTHCOMING AS TO WHO AND WHY THIS CONFLICT OCCURRED. BOTH PLTS ESTIMATED WE PASSED DIRECTLY OVER THE OTHER ACFT WITH A VERTICAL CLRNC OF APPROX 400 FT. IT WAS OUR CONSIDERED OPINION THAT THIS WAS A CTLR ERROR WHICH COULD HAVE BEEN CATASTROPHIC WITHOUT THE TCASII SYS.