AN ACR PASSED APPROX 200 FT OVER ANOTHER ACR AS HE WAS LNDG ON A RWY WHOSE APCH PATH EXTENDED OVER THE RWY THAT WAS BEING USED FOR DEPARTURES.

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CAPT WAS MAKING TKOF FROM 32L AT T10. TWR CLRED US FOR TKOF WITH A TURN TO 330 DEGS. TKOF WAS NORMAL UNTIL I NOTICED A 757 ON SHORT FINAL FOR 9L AT OUR 10:30 POS. WE WERE BTWN 100-120 KNOTS AT THE TIME. OUR V1 WAS 137 AND OUR VR WAS 139. CAPT ELECTED TO CONTINUE TKOF ROLL BUT TO DELAY ROTATION UNTIL WE WERE BEYOND THE 757'S FLT PATH. WE DID NOT NOTICE ANY CHANGE IN 757 FLT PATH TOWARDS 9L. ONCE WE HAD CLRED THE 757'S FLT PATH THE CAPT ROTATED AT ABOUT 170 KNOTS WITH ABOUT 2000 FT OF RWY REMAINING. REST OF CLIMB OUT/CLEANUP WAS UNEVENTFUL AND TWR HANDED US OFF TO DEP. I THINK THAT OUR DELAYED ROTATION AND CONTINUED ACCELERATION PROBABLY KEPT US IN FRONT OF THE ARRIVING 757 BUT HAD WE ROTATED NORMALLY WE WOULD HAVE COME VERY CLOSE TO A COLLISION. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE ACFT WERE BEING CONTROLLED BY SEPARATE ATCT LOCAL CTLRS ON SEPARATE FREQUENCIES. THE DEPARTING ACFT WAS HELD IN POS WAITING FOR WAKE TURB SEPARATION FROM A PRECEDING HEAVY ACFT DEP. NEITHER ACFT WAS ADVISED OF THE OTHER. THE ARRIVING ACFT WAS GIVEN HIS LNDG CLRNC APPROX 10 MILES OUT ON FINAL. HE WAS RECEIVING PRIORITY HANDLING DUE TO A MEDICAL EMER. HIS RWY ASSIGNMENT WAS FOR EXPEDITED HANDLING TO HIS TERMINAL. IT WAS NOT IN USE BY OTHER LNDG TFC. THERE WAS NO OPERATIONAL REASON WITH THE ACFT THAT WOULD PREVENT HIM FROM EXECUTING GAR. DURING AFTER THE FACT CONFERENCE WITH TWR SUPERVISION BY ONE OF THE CREWS; IT WAS RPTED THAT THE CTLR OF THE TKOF RWY CALLED FOR THE OTHER CTLR TO SEND THE LNDG ACFT AROUND. HIS REQUEST WAS DENIED/OVERRIDDEN BY TWR SUPERVISION WHO THOUGHT IT 'LOOKS BAD BUT WOULD WORK OUT.' WHEN THE OTHER CREW CONFERRED WITH TWR THEY WERE TOLD THAT 'IT WAS UGLY BUT IT LOOKED LIKE IT WOULD WORK OUT.' SUPPLEMENTAL INFO FROM ACN 515087: AFTER TKOF CLRNC RECEIVED TKOF ROLL WAS NORMAL UNTIL THE 9L 757 WAS SEEN ON SHORT FINAL. TO AVOID CLBING INTO HIS FLT PATH I DID NOT ROTATE AT VR BUT CONTINUED TO ROLL DOWN THE RWY XING UNDER HIM ON THE EXTENDED 9L CENTERLINE. MY VR WAS 139 -- I ROTATED ABOUT 170 WITH APPROX 2000 FT OF 32L REMAINING. MY THOUGHTS AT THE TIME WERE: IF I ROTATE I WILL HIT HIM. I'M TOO FAST TO ABORT. WILL HE SEE ME AND GAR? WILL HE PASS OVER ME SAFELY? DO I HAVE ENOUGH ROOM TO ROTATE BEFORE THE END OF THE 32L RWY ENDS? SUPPLEMENTAL INFO FROM ACN 515192: ON SHORT FINAL TO 9L AN MD80 PASSED APPROX UNDER US AS HE WAS MAKING HIS TKOF FROM 32L. WE WERE GIVEN ATC PRIORITY HANDLING INTO ORD BECAUSE OF A MEDICAL EMER. THE TIMING OF THE 32L DEP WAS A LITTLE OFF WHICH RESULTED IN THE MD80 BEING APPROX UNDER OUR FLT PATH WHILE ON HIS TKOF ROLE. AGGRESSIVE CONTROLLING MIGHT HAVE BEEN OR MISCOMMUNICATION BTWN TWR CTLRS. I DON'T FEEL IT WAS UNSAFE; BUT A LITTLE CLOSER THAN IT SHOULD HAVE BEEN. I WAS THE CAPT OF THE FLT AND THE PLT FLYING. I DON'T BELIEVE THAT EITHER I; THE FO; OR THE FAA INSPECTOR ON THE JUMP SEAT SAW THE MD80 UNTIL WE WERE BASICALLY PASSING OVER HIM. I DON'T KNOW IF THE OTHER AIRPLANE SAW US OR NOT. NOTHING WAS SAID ON THE TWR FREQ. WE WERE GIVEN TAXI CLRNC TO OUR GATE BY TWR SO WE WERE ON THE FREQ FOR AWHILE. WE HAD A FEMALE PAX WITH ABDOMINAL PAIN AND HAD ARRANGED FOR EMT'S TO MEET US AT OUR GATE. WE HAD BEEN WORKING THIS PROB FOR 2-3 HRS AND HAD BEEN IN CONTACT WITH OUR DISPATCH; COMPANY DOCTOR; AND ATC REGARDING THIS SIT. A DOCTOR AND NURSE ON BOARD WERE ATTENDING TO THE LADY. DISPATCH; THROUGH OUR ATC COORDINATION HAD ARRANGED FOR PRIORITY HANDLING INTO O'HARE.