FK10 FLC TURNS TO WRONG HDG AFTER DEP WHEN INCORRECTLY HEARING CLRNC.

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OUR ACFT WAS CLRED TO TKOF FROM ORD; FOLLOWED BY A R TURN TO A 010 DEG HDG AFTER DEP. WE COMPLIED WITH THE CLRNC. TWR THEN INSTRUCTED US; 'ON A HDG OF 010 DEGS CONTACT DEP ON 125.00.' THE TWR CTLR HAD RESTATED A HDG THAT WE HAD ALREADY RECEIVED IN THE TKOF CLRNC. I HAD BEEN ANTICIPATING A TURN TO THE R. SO I BELIEVED THAT I HAD HEARD TWR CTLR ISSUE US A TURN TO A 040 DEG HDG AND CONTACT DEP. I ACKNOWLEDGED THE TWR'S INSTRUCTION WITHOUT A READBACK. I THEN CONTACTED THE DEP CTLR AND TOLD HIM THAT WE WERE CLBING OUT OF 2200 FT FOR 5000 FT AND IN A R TURN TO 040 DEG HDG. THE DEP CTLR ACKNOWLEDGED WITH 'RADAR CONTACT; CLB AND MAINTAIN 6000 FT.' THE DEP CTLR DID NOT CATCH OUR HDG CHANGE READBACK TO 040 DEGS BECAUSE HE DID NOT ISSUE THE HDG CHANGE AND DIDN'T EXPECT IT. LATER IN THE CLBOUT DEP ASKED US OUR HDG TODAY. I REPLIED WITH 'THEY ASSIGNED US 040 DEGS;' WHICH I BELIEVED THEY HAD. DEP THEN INSTRUCTED US TO TURN TO 070 DEGS. THE PROB AROSE WHEN TWR RESTATED A HDG THAT WE HAD ALREADY BEEN ISSUED. I ANTICIPATED A R TURN; AND I READ BACK THE BELIEVED HDG CHANGE TO THE DEP CTLR; WHO WAS NOT EXPECTING IT. IN THE FUTURE ATC INSTRUCTION SHOULD BE READ BACK TO THE ISSUING CTLR AND NOT TO THE NEXT ASSIGNED CTLR. SUPPLEMENTAL INFO FROM ACN 331706: WE WERE ANTICIPATING FAIRLY RAPID TURNS TO THE E AS IS TYPICAL LEAVING O'HARE HEADING TOWARDS ELX. SOMEHOW WE HAD 040 DEGS IN OUR HEAD. HOW COULD IT POSSIBLY HAPPEN? AN ATR CLRED FOR TKOF ON RWY 32R JUST PRIOR TO US WAS GIVEN AN IMMEDIATE R TO 040 DEGS; AND WHEN ORD TWR GAVE US THE HDOF TO DEP ON 125.0 AND RESTATED THE HDG OF 010 DEGS (WE WERE ALREADY WELL ESTABLISHED ON 010 DEGS) THIS COULD HAVE TRIGGERED US BELIEVING WE WERE INSTRUCTED TO TURN TO 040 DEGS. TWR RESTATING A PREVIOUSLY ISSUED HDG I FEEL IS A LITTLE UNUSUAL.