B737 FLT CREW ATTEMPTS TO TAKE OFF USING ANOTHER ACFT'S CLRNC AND REJECTS THE TKOF WHEN THE OTHER ACFT IS OBSERVED ROLLING ON A XING RWY AT MDW.

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WE WERE CLRED INTO POS AND HOLD ON RWY 4R AT MDW. I CALLED FOR THE BELOW THE LINE CHKLIST. AS WE WERE TAXIING ONTO THE RWY; DOING THE CHKLIST; WE HEARD TWR TELL US TO TURN L TO A HEADING; WHICH I MISSED; AND CLRED FOR TKOF. THE FO REPLIED; 'COMPANY NUMBER TURN L TO 025 DEGS AND CLRED FOR TKOF.' I WASN'T SURE OF THE HEADING; SO I QUESTIONED THE FO. HE STATED THAT IT WAS 025 DEGS AND HAD ALREADY SET 025 DEGS IN THE HEADING SELECT WINDOW. I ADVANCED THE THRUST LEVERS AND PUSHED UP TOWARD TKOF THRUST; AS I CALLED SET TKOF THRUST; I SAW A COMPANY AIRPLANE ROLLING THROUGH THE INTXN; TAKING OFF ON RWY 31C. I IMMEDIATELY REALIZED THAT WE HAD ACCEPTED HIS TKOF CLRNC AND ABORTED THE TKOF. THE TWR NOTICED US ROLLING ON RWY 4R AND ASKED US TO CLR THE RWY. AN AIRPLANE WAS TAXIING ON TXWY Y APCHING TXWY K; SO WE TAXIED UP TO; AND CLRED; AT RWY 31L. THE AIRSPD HAD NOT YET COME OFF THE PEG WHEN WE ABORTED AND A CHK OF THE OPC INDICATED THAT WE DID NOT HAVE A BRAKE COOLING PROB; SO WE TAXIED BACK TO RWY 4R AND MADE AN UNEVENTFUL TKOF. WHEN I GOT TO TPA I CALLED THE MDW TWR AND HE SAID THAT THE OTHER FLT'S XMISSION HAD OVERRIDDEN OURS. I THINK SEVERAL THINGS CONTRIBUTED TO THIS INCIDENT: SIMILAR SOUNDING CALL SIGNS AND USING XING RWYS. THE CALL SIGNS WERE SIMILAR AND EASY TO CONFUSE; ESPECIALLY WHILE DOING THE CHKLIST. I DON'T KNOW IF WE WERE STILL ON GND FREQ WHEN THE OTHER FLT WAS CLRED ONTO RWY 31C; BUT AN ADVISORY OF TFC DEPARTING RWY 31C WHEN WE WERE CLRED ONTO RWY 4R WOULD HAVE HELPED. THIS ALSO EMPHASIZES THE NEED TO 'LISTEN UP;' PARTICULARLY WHEN THE ARPT IS USING XING RWYS. I ALSO SHOULD HAVE HAD THE FO RECONFIRM THE HEADING WITH THE TWR; THAT WOULD HAVE GOTTEN US ALL ON THE SAME GAME PAGE. I CERTAINLY WILL NOT HESITATE TO RECONFIRM ANY CLRNCS THAT I HAVE THE SLIGHTEST DOUBT ABOUT FROM NOW ON. SUPPLEMENTAL INFO FROM ACN 579210: THE REST OF THE FLT WAS UNEVENTFUL. I BELIEVE I MISTAKENLY READ BACK COMPANY NUMBER'S TKOF CLRNC; AND WHEN I READ IT BACK; TWR DIDN'T HEAR ME BECAUSE I WAS CUTOUT BY COMPANY READING BACK HIS TKOF CLRNC. THE CALL CAME RIGHT IN THE MIDDLE OF THE 'BELOW THE LINE' PORTION OF THE PRE TKOF CHKLIST; AND I SHOULD HAVE NOTICED THE 025 DEG HDG LOOKED UNUSUAL (POINTED TO THE N SIDE OF DOWNTOWN). LESSONS LEARNED: PRIORITIZE. IF GIVEN A CLRNC FOR TKOF (AT A HIGH VOLUME ARPT; WITH XING RWYS; OR MULTIPLE PARALLEL RWYS); WHILE ACCOMPLISHING THE REMAINDER OF THE PRE TKOF CHKLIST; FINISH THE CHKLIST; THEN RESPOND TO THE TKOF CLRNC. ANYTIME THERE IS A QUESTION ABOUT A HEADING; ALT; OR CLRNC; QUERY THE CTLR. RADIO CALLS ARE FREE!