C501 CREW DEPART ORD WITHOUT A TKOF CLRNC AFTER TAXI INTO POS AND HOLD CLRNC.

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I WAS ACTING PIC ON A NEWLY LEASED CITATION ONE. MY CO-CAPT HAD MADE ONE PREVIOUS TRIP IN THE ACFT. WE WERE CLRED TO TAXI OUT TO RWY 32 AND MY COPLT RAN TAXI CHKLISTS; AND PROGRAMMED THE GPS. WE HAD BEEN EXPERIENCING PROBS WITH THE COPLT'S RADIO JACK; SO HE WAS XMITTING OVER THE HEADSET AND LISTENING ON THE SPEAKER. I STUDIED THE SID AND BRIEFED THE COPLT AND HE CALLED CHICAGO TWR TO ADVISE THEM WE WERE READY TO DEPART. IT WAS A GOOD VMC DAY WITH VERY GUSTY WINDS AND FAIRLY LIGHT TFC. RWYS 27L/R AND 32 WERE IN USE. I TAXIED ONTO THE RWY WHILST THE COPLT READ BACK THE TWR'S CLRNC TO TAXI AND REMAIN CLR OF RWY 27R. I WAS PREOCCUPIED WITH MAKING SURE I STAYED CLR OF RWY 27R AND REMAINED ON THE CORRECT RWY AS WE WERE PERFORMING AN INTXN DEP; THAT I ONLY PARTIALLY COPIED THE TWR'S INSTRUCTIONS. I TAXIED INTO POS ON RWY 32 AND MY COPLT TOLD ME WE WERE CLRED TO TAKE OFF. I ASKED HIM 'ARE YOU SURE? WHAT HEADING.' HE SAID; 'YES; WE'RE CLR TO GO.' I SHOULD HAVE ASKED HIM TO CALL TWR AND CLARIFY; BUT I DIDN'T. WE ROLLED DOWN RWY 32; ROTATED AND CLBING THROUGH 300 FT; TWR CALLED AND SAID THAT WE HAD NOT BEEN RELEASED AND TO TURN R HEADING 040 DEGS. THE COPLT REPLIED WITH THE HEADING CHANGE AND WE CONTINUED THE CLB WITH A HDOF TO DEP. AT CRUISE ALT; I ASKED THE COPLT IF HE FELT THAT WE HAD BEEN 'CLRED FOR TKOF' AND HE REPLIED 'YES.' I FEEL VERY NEGLIGENT AS PIC OF THE ACFT THAT I DID NOT ASK FOR CLARIFICATION FROM TWR OF A TKOF CLRNC. I REALIZE THAT WE WERE VERY FORTUNATE THAT WE DID NOT CAUSE A RWY INCURSION. I HAVE ALWAYS MAINTAINED A GOOD SAFETY RECORD AND FEEL THIS HAS BEEN A HUGE REALITY CHK AND NEVER AGAIN WILL I IGNORE MY BETTER JUDGEMENT TO QUESTION ANY DOUBTFUL DECISIONS. I REALIZE THAT AN ACCIDENT IS CAUSED BY A CHAIN OF EVENTS. OURS WERE: 1) A RENTED ACFT WITH A FAULTY HEADSET JACK; 2) DEPARTING FROM A RWY INTXN WITH AN UNCLR TWR XMISSION; 3) FAILURE TO VERIFY A TKOF CLRNC; AND 4) FAILURE TO COMMUNICATE EFFECTIVELY AS A CREW.