AN ACR MD80 SUFFERS A HDG DEV AND A POTENTIAL CONFLICT WITH ANOTHER ACR HVY ON APCH TO RWY 27L AT ORD.

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AT 5000 FT ON DOWNWIND TO ILS RWY 27L AT ORD I HEARD AND FO HEARD AND READ BACK INSTRUCTIONS TO TURN TO 010 DEGS; DSND TO 4000 FT. WHILE ROLLING OUT ON 010 DEG HDG AT ABOUT 4500 FT WE GOT A 'TFC' ALERT ON TCASII FOLLOWED SHORTLY BY AN RA 'MONITOR VERT SPD.' AT THE SAME TIME WE GOT INSTRUCTIONS TO TURN TO 120 DEGS; MAINTAIN 5000 FT. I DISENGAGED THE AUTOPLT AND MADE A CLBING TURN TO 120 DEGS AND 5000 FT. AT ABOUT THE TIME OF THE RA AND INSTRUCTIONS TO TURN TO 120 DEGS WE ACQUIRED VISUAL CONTACT WITH A HVY. MY BEST GUESS WOULD BE THAT HE WAS ABOUT 500 FT BELOW US AT A RANGE OF ABOUT 1 MI. DURING THE TURN TO 120 DEGS THE CTLR SAID WE HAD BEEN ASSIGNED A HDG OF 100 DEGS. THE FO AND I WERE BOTH SURE WE HEARD 010 DEGS; AND THAT IS WHAT WAS READ BACK BY THE FO. MAYBE WE JUST HEARD WHAT WE EXPECTED TO HEAR AT THIS POINT ON THE APCH AND THE CTLR DIDN'T CATCH OUR READBACK. AFTER FILLING OUT THE OTHER SIDE OF THIS FORM I CALLED ORD TRACON AND SPOKE WITH A SUPVR. HE SAID THE TAPES HAD BEEN REVIEWED AND THAT MY FO HAD READ BACK A HDG OF 100 DEGS. I'M SURE THE FO WILL BE AMAZED BY THAT AS AFTER THE INCIDENT HE WAS POSITIVE HE HAD READ BACK 010 DEGS. I FIND IT VERY HARD TO UNDERSTAND HOW THIS HAPPENED. I ALWAYS REPEAT ALL ASSIGNED HEADINGS AND ALTS TO BE SURE THAT THE FO AND I AGREE ON WHAT WE HEARD. SOMEHOW THIS TIME EVEN THOUGH THE FO READ BACK 100 DEGS TO THE CTLR WE WERE BOTH 'THINKING' 010 DEGS. IN THE PAST I HAVE EXPERIENCED TIMES WHERE THE FO OR MYSELF WOULD MISTAKE 010 DEGS; 020 DEGS; OR 030 DEGS FOR 100 DEGS; 200 DEGS; 300 DEGS BUT ONE OF US ALWAYS CORRECTED OR QUESTIONED THE OTHER AND THE HEADING WAS RECONFIRMED WITH THE CTLR. THIS TIME NEITHER OF US HAD ANY DOUBT WE WERE CORRECT WHEN IN FACT WE WERE WRONG. I REALLY HAVE NO SUGGESTIONS ON HOW TO AVOID THIS IN THE FUTURE. I WILL CERTAINLY REDOUBLE MY EFFORTS TO BE SURE ALL CLRNCS ARE HEARD CORRECTLY. THE TRACON SUPVR SAID HE WOULD HAVE TO FILE A RPT ON LOSS OF SEPARATION AS WE WERE AS CLOSE AS 500 FT AND 2 MI TO THE OTHER ACFT. THE TCASII WORKED AS IT SHOULD AND WOULD HAVE KEPT US FROM GETTING ANY CLOSER TO THE OTHER ACFT IF THE CTLR HAD MISSED THE SIT.