AN ACR MLG CLBED AND TURNED IN RESPONSE TO A TCASII COMMAND.

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I WAS VECTORING ACFT OUT OF HOLDING PATTERN AIRSPACE SE OF CHICAGO O'HARE FOR 20 MI INTRAIL SPACING. ACR MLG WAS 15 NM S OF THE HOLDING PATTERN AT 12000 FT MSL. I TURNED MLG R TO A HDG OF 350 DEGS AND DSNDED THE ACFT TO 11000 FT MSL. MLG READ THE CLRNC BACK CORRECTLY. I OBSERVED MLG AT 11900 FT INDICATING TO ME THAT THE ACFT HAD STARTED ITS DSCNT. LGT IN THE HOLDING PATTERN WAS THEN DSNDED FROM FL140 TO FL120. I WENT ON TO SOME COORD WITH ORD TWR AND SURROUNDING SECTORS. WHEN I LOOKED BACK MLG WAS BACK UP AT FL120 ALONG WITH LGT. I ATTEMPTED TO TURN AND DSND MLG AND CLB LGT BUT THE ACFT WERE ALREADY RESPONDING TO TCASII RA'S. SEPARATION WAS LOST; THE ACFT PASSED WITH 1.6 NM AND 700 FT AT THEIR CLOSEST POINT. SUPPLEMENTAL INFO FROM ACN 236215: WE RECEIVED AN RA FROM TCASII INDICATING A 'MONITOR VERT SPD' AT WHICH TIME WE COMPLIED WITH A CLB AND ALSO INITIATED A L TURN AS THE OFFENDING LGT WAS IN SIGHT VISUALLY AHEAD AND TO THE R. THE CTLR ASKED US IF THE PREVIOUS CTLR HAD CLRED OUR FLT TO 11000 FT. WE RESPONDED THAT WE HAD NOT RECEIVED ANY SUCH CLRNC AND THAT THE LAST ALT CLRNC WAS TO 12000 FT.