MD80 CREW AND A LEARJET HAD LESS THAN LEGAL SEPARATION IN ZAU CLASS A.

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NEAR MISS. RESPONDED TO AN RA CLBING THROUGH FL205. RA ISSUED WAS CLB; THEN IMMEDIATELY FOLLOWED BY 'CLB; CLB NOW.' TCASII COMMANDED A 2000 FPM CLB WHICH WAS FOLLOWED. IT WAS NECESSARY FOR THE SIT; BUT DID NOT CONFLICT WITH ATC'S INSTRUCTIONS AS WE WERE IN A CLB TO FL230. NO CLRNC DEV RESULTED; NO INJURIES. THE VERT DISTANCE WAS 400 FT; UNDER THE ACFT'S NOSE. THE ACFT WAS A LEARJET. DISPATCH WAS CONTACTED AND GIVEN THE INFO THEY REQUESTED. ZAU; MGR ON DUTY; WAS CONTACTED AND GIVEN THE INFO THEY REQUESTED. A PLT EVENT QUESTIONNAIRE WAS FILLED OUT. FOR CTLED AIRSPACE THIS WAS NEAR FATAL AND TOTALLY UNACCEPTABLE. ADDITIONAL INFO. IN CLBOUT GOING THROUGH FL205; OBTAINED TCASII TA IMMEDIATELY FOLLOWED BY RA TO CLB; THEN CLB; CLB NOW. AUTOPLT DISCONNECTED AND FOLLOWED TCASII CLB COMMAND OF 2000 FPM PASSING TO R OF OUR ACFT. TCASII INDICATED ACFT LEARJET PASSED 400 FT BELOW WITH LESS THAN 1 MI HORIZ SEPARATION. THE RA WAS FOLLOWED; IT WAS NECESSARY FOR THE SIT; IT DID NOT CONFLICT WITH ATC INSTRUCTIONS NOR DID IT RESULT IN A CLRNC DEV. ATC WAS ADVISED OF THE RA AND WAS TOLD WE WOULD BE FILING A NEAR MISS RPT. THE RPT WAS FILLED WITH ZAU. SHORTLY AFTER THE INCIDENT; DISPATCH WAS NOTIFIED OF THE NEAR MISS AND THE REQUESTED INFO WAS EXCHANGED.