ACR Y READ BACK AND FLEW WRONG HDG HAD LTSS FROM ACR X. SYS ERROR.

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ACR X LEVEL AT 8000 FT; WBOUND ON THE PULLMAN ARR (HDG 270 DEGS ASSIGNED) WHEN I OBSERVED EBOUND TFC AT 12:00- 12:30 O'CLOCK NEAR OR SLIGHTLY BELOW OUR ALT. THE NIGHT WAS VERY DARK BUT AT THE SAME TIME THE AIR WAS VERY CLR. THE TFC APPEARED TO BE SOME MILES AWAY. I ASSUMED IT WAS VFR TFC AT 7500 FT. AS THE TFC MOVED NEARER IT BECAME OBVIOUS IT WOULD PASS OFF OUR R WING AND SLIGHTLY BELOW US. SIMULTANEOUSLY; ATC GAVE US A TFC RPT AND IMMEDIATE L TURN TO 180 DEGS AND DSCNT TO 7000 FT. ON THE GND; I TALKED TO THE APCH CTL SUPVR WHO SAID THAT ON HIS INITIAL INVESTIGATION IT LOOKED AS IF ACR Y WAS GIVEN A 280 DEG HDG BUT INSTEAD TURNED AROUND TO 080 DEGS. NOTES: 1) ACR X WAS NOT TCASII EQUIPPED. 2) I BELIEVE ATC TWICE TRIED TO ISSUE TA'S BUT EACH TIME WAS BLOCKED BY NUMEROUS XMISSIONS FROM OTHER ACFT. 3) TFC INTO ORD WAS VERY HVY AND THE RADIO FREQ WAS SATURATED. SUPPLEMENTAL INFO FROM ACN 228943: I WAS WORKING ORD APCH CTL DURING HVY INBOUND EBOUND RUSH. I WAS TRAINING A DEVELOPMENTAL AT THE TIME. O'HARE WAS LNDG RWYS 14L/R. WE WERE VECTORING TO RWY 14L. ACR Y WAS 20 MI NE OF ORD HDG 220 DEGS ON PULLMAN 1 ARR. WE GAVE ACR Y A 'TURN R HDG 280 DEGS.' WE BELIEVED ACR Y TO ACKNOWLEDGE HDG. APPROX 1.5 MINS LATER; ACR Y IS HDG EASTERLY INTO HVY INBOUND E ARR FIX AT 8000 FT. ACR X WAS INBOUND FROM SAME FIX ALSO AT 8000 FT. I GAVE ACR X AN IMMEDIATE TURN (SBOUND) AND DSCNT. ACR X SAID HE HAD VISUAL CONTACT WITH ACR Y. I TOLD ACR X TO MAINTAIN VISUAL SEPARATION AND THEN TURNED ACR Y NBOUND AWAY FROM ACR X. AS IT TURNED OUT; ACR Y THOUGHT WE GAVE HIM A 080 DEG HDG AS OPPOSED TO A 280 DEG HDG. THE READBACK WAS SOMEWHAT DIFFICULT TO DISTINGUISH BECAUSE IT WAS READ BACK VERY QUICKLY. AT THE TIME; IT SOUNDED LIKE A 280 DEG HDG IN THE READBACK. ON TAPE AFTERWARDS; AFTER 3 OR 4 TIMES LISTENED TO; IT WAS DETERMINED TO BE A 080 DEG HDG IN ACR Y READBACK.