POTENTIAL CONFLICT BTWN OPPOSITE DIRECTION DSNDING TFC.

Narrative

WE WERE APPROX 10 MI FROM KRENA INTXN ON ARR TO ORD. WE WERE CLRED TO 10000 FT AND WERE THROUGH 14000 FT WHEN ATC TOLD US TO EXPEDITE TO 12000 FT. WE RECONFIRMED THAT 12000 FT WAS OUR NEW CLRNC LIMIT AND IT WAS CONFIRMED. JUST AFTER THIS POINT WE GOT A TCASII RA ALERT FOR TFC AT OUR 12.00 POS -- THE RA DIRECTED A DSCNT -- WE HAD THE ACFT IN SIGHT AND IT APPEARED TO BE AT OUR ALT AND DSNDING. OUR TCASII CHANGED TO CLB RA WHICH WE RESPONDED TO AND CLBED TO APPROX 12-800 FT THEN RETURNED TO 12000 FT AFTER THE RA EVENT. WE NOTIFIED ATC OF OUR RESPONSE TO THE RA AND THAT WE HAD CLBED. THE TFC APPEARED TO GET WITHIN LESS THAN A MI OF OUR POS AT OUR ALT. SUPPLEMENTAL INFO FROM ACN 297859: WE THEN SAW AN AIRPLANE AT 12 O'CLOCK ABOUT 5 NM AND IT APPEARED ABOVE AND TCASII SAID IT WAS DSNDING. WE GOT A RA; THE CAPT RESPONDED BY REMAINING VISUAL AND WHEN IT GAVE US A CLB HE INITIATED A CLB AS I INFORMED CTR. THE AIRPLANE PASSED ABOUT 1 NM AND 500 OR MORE FT BELOW US AS WE CLBED TO 12-800 FT. WE REMAINED IN VISUAL CONTACT WITH THE OTHER ACFT AT ALL TIMES DURING THE RA.