AN MLG FLEW THE WRONG HDG AFTER TKOF. ALL 3 PLTS HEARD 065 VICE THE 165 THAT DEP CTL CLAIMS TO HAVE ISSUED.

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WE WERE DEPARTING ON FLT FROM CLT TO PHL. WE WERE TO NAV ON THE 076 DEG RADIAL OF CLT TO MERIL. WE TOOK OFF RWY 18L AND FLEW RWY HDG AND WENT OVER TO DEP CTL. THEY ISSUED A 065 DEG HDG. THE COPLT READ BACK 065 DEG HDG AND WE STARTED THE TURN. ON THE COLLISION AVOIDANCE SCREEN WE NOTICED SOME HIGHER TFC INBOUND. WE CALLED DEP CTL BACK TO VERIFY HDG. WE GOT NO RESPONSE AFTER 3 CALLS. I STOPPED THE TURN AT 120 DEG AND THEN THE CTLR CALLED US TO LEVEL OFF SO WE WOULD HAVE 1000 FT SEPARATION. WE LEVELED OFF AND HAD 1000 FT SEPARATION ON SCREEN. THE CTLR THEN SAID HE HAD ISSUED A 165 DEG HDG. WE TOLD HIM WE READ BACK 065 DEG. WE ASKED HIM IF THERE WAS A CONFLICT AND HE SAID NO! WE WERE THEN GIVEN A HDG TO INTERCEPT THE 076 DEG RADIAL AND PROCEEDED ON COURSE. SUPPLEMENTAL INFO FROM ACN 219103: DEP CTL CALLED US WITH A LOWER ALT TO CLB TO FOR CONFLICTING TFC. DEP CTL STATED THE HDG SHOULD HAVE BEEN 165 DEG. ALL 3 PLTS; CAPT; COPLT; JUMPSEAT; STATED THEY HEARD 065 DEG HDG ISSUED. DUE TO THE SLOW RESPONSE OF DEP CTL (3 CALLS) ANY CONFLICT OF HDG WOULD HAVE BEEN AVOIDED.