A B737-300 CAPT STATED THAT ZAU WAS TOO CASUAL IN HIS SUGGESTION THAT THE RPTR STOP HIS DSCNT TO AVOID A VFR CITATION WHICH HAD NOT YET APPEARED ON HIS TCASII.

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DSNDING ON THE BVT2 ARR INTO MDW WITH A XING RESTR OF 11000 FT AT OXFAT INTXN; WE WERE BEGINNING A L TURN TO JOIN THE ARR WHEN ZAU VERY CASUALLY SUGGESTED WE LEVEL OFF AT 17000 FT AND LET VFR TFC GO UNDER US AT 16500 FT. I (PNF); STILL MONITORING ATC; AND TRYING TO GET ATIS FOR THE THIRD TIME; LOUD SQUEAL ON FREQ WHICH I HAVE RPTED TO APCH ON SEVERAL OCCASIONS; OVERHEAR THE ATC'S SUGGESTION. MY ATTN IMMEDIATELY FOCUSED ON THE TCASII DISPLAY. TO MY SURPRISE; IT SHOWED NO TARGETS. THE TCASII WAS ON 15 MI AND BELOW. MY FO (PF) SHALLOWED OUR DSCNT AS A PRECAUTION WHILE WE BOTH MONITORED THE TCASII AND OUTSIDE. AS WE ROLLED OUT ON THE ARR HDG; WE WERE BOTH SURPRISED WHEN THE TCASII GAVE US AN RA TO CLB; CLB. I LOOKED AT THE TCASII AND SAW A 3 MI TARGET AT 12 O'CLOCK POS; 900 FT BELOW. WE DID NOT HAVE TIME TO CLB; ALL WE HAD TIME TO DO WAS STOP THE DSCNT. A CITATION 10 PASSED UNDERNEATH US AT APPROX 700 FT AND 1/4 MI ON OUR R. IT APPEARED THE CITATION WAS CRUISING VFR AT 16500 FT IN EXCESS OF 300 KTS; WHILE NOT IN ATC COM. WE WERE AT 280 KTS; AND DSNDING AT 2500 FPM. AT THAT ALT; THE CLOSURE RATE WAS APPROX 700 MPH. IN CONCLUSION: 1) APPARENTLY ATC DID NOT REALIZE WE DID NOT HAVE THAT TARGET ON OUR TCASII DISPLAY. WE NEED TO ADVISE ATC THAT NOT ALL TARGETS ARE DISPLAYED ON OUR TCASII SCREENS. 2) I WILL NO LONGER SPEND EXTRA TIME TRYING TO RECEIVE ATIS FROM A BAD FREQ; AND WILL NOT ATTEMPT TO RECEIVE ATIS OUTSIDE CLASS A AIRSPACE. 3) APPARENTLY; OUR XPONDER ANTENNA DID NOT RECEIVE THE CITATION'S XPONDER BECAUSE OF ANTENNA POS. THIS NEEDS TO BE ADDRESSED BY THE FAA.