A B737 CREW; TAXIING TO THE GATE AT ORD; HAD A CLOSE ENCOUNTER WITH ANOTHER ACFT; AS BOTH CREWS MAINTAINED EACH HAD THE RIGHT OF WAY.

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FROM THE PENALTY BOX; I HAD TO RETURN TO THE GATE FOR AN ACFT MALFUNCTION. ORD GND SAID TO TAKE TXWY B TO THE GATE. TAXIING TO THE GATE RAMP ASSIGNED ME GATE TO PULL INTO. PRIOR TO REACHING A15 ON TXWY B I STOPPED AND WAITED FOR A B777 TO TAXI INTO OTHER GATE. HE WASN'T MOVING SO I TOLD THE COPLT TO TELL RAMP THAT I WANTED TO GO TO THE GATE NOW. THEY SAID OK. AS I TURNED L ONTO A15 TO CROSS TXWY A TO THE GATE; OUT OF THE CORNER OF MY EYE I SEE AN ACFT AT MY 3 O'CLOCK POS AT ABOUT 300 FT TAXIING FAST TOWARDS ME. I THOUGHT TO MYSELF SURELY OTHER ACFT SEES ME AND WILL SLOW DOWN OR STOP. AS I CONTINUE TO TAXI FORWARD; TOO LATE TO STOP; I SEE ACFT CONTINUING HIS SAME SPD AND NOT SLOWING AT ALL. I AM CONCERNED AND CONTINUED TO TAXI. NO TIME TO XMIT TO GND OR ACFT. FINALLY GND SAYS; TO THE EFFECT; 'BOY THE FAA WOULD HAVE LOVED THAT;' AND OTHER ACFT COMES BACK AND SAYS FLIPPANTLY 'OH IT HAPPENS ALL THE TIME.' IN MY ESTIMATION OTHER ACFT CAME VERY CLOSE TO MY ACFT AND BY HIS MANNER I BELIEVE HE WAS PLAYING CHICKEN AND I DON'T LIKE IT AND THAT IS WHY I'M SENDING THIS RPT. AT CHICAGO WE ARE GOING TO HAVE A GND ACCIDENT BECAUSE OF FAST TAXI SPDS AND FOLLOWING ACFT TOO CLOSE AND JUST CUTTING IT TOO CLOSE FOR COMFORT. SUPPLEMENTAL INFO FROM ACN 543659: AS I LOOKED UP; SAW OUT OF THE CORNER OF MY R EYE; AN ACR RJ FAIRLY CLOSE; 300 FT; BUT MOVING VERY FAST TOWARD US. AT THE SAME TIME I WAS SELECTING ORD GND AGAIN JUST IN TIME TO HEAR GND CTLR SAY SOMETHING LIKE; 'THAT WASN'T THE SMOOTHEST MOVE I'VE SEEN.' I BELIEVE HE WAS IMPLYING WE HAD CUT IN FRONT OF THE RJ. I DON'T FEEL THIS WAS THE CASE SINCE; WE HAD BEEN PREVIOUSLY TOLD 'TXWY B TO THE GATE;' AND HAD THE EAGLE BEEN TAXIING AT A SAFER SPD; THE FINAL DISTANCE BTWN US WOULD HAVE BEEN A NON-ISSUE.