B737 CREW TAXIING TO RWY 4 AT MDW WERE INSTRUCTED TO HOLD SHORT OF RWY 31. WHEN THE TAXI INSTRUCTIONS WERE RECEIVED BY THE FO; THE PIC WAS STILL PLUGGED IN WITH THE PUSHBACK CREW AND DID NOT HEAR THE CLRNC.

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HERE IS WHERE THE TROUBLE BEGAN -- I WAS LATE SWITCHING FROM THE FLT INTERCOM (RAMP) TO GND AND THE FO WAS QUICK TO CALL FOR TAXI -- HENCE; I MISSED THE INSTRUCTIONS TO HOLD SHORT OF A XING RWY AND I NEVER HEARD THE READBACK. I WAS PREOCCUPIED WITH THE INITIAL TAXI AWAY FROM THE GATE AND A REQUIREMENT TO 'GIVE WAY' TO AN INBOUND KING AIR. THIS ACT OF GIVING WAY REQUIRED ME TO MOVE THE ACFT AWAY FROM MY DIRECTION OF TAXI; AND AFTER OUR 'MINUET' WAS COMPLETED; I HEADED FOR THE TKOF RWY. AS I APCHED THE XING RWY IN QUESTION; I 'CLRED' IT VISUALLY AND NOTICED THAT AN AIRPLANE WAS LNDG ON THE RWY TO WHICH I WAS TAXIING AND SINCE IT WAS LNDG PARALLEL AND OPPOSITE TO MY DIRECTION OF TAXI; I GAVE NO THOUGHT AT ALL TO A HOLD SHORT REQUIREMENT. ABOUT THEN; GND CAME UP AND STATED; 'YOU WERE SUPPOSED TO HOLD SHORT; BUT SINCE YOU'RE ALREADY ON THE RWY; CONTINUE TO TAXI.' AS SOON AS I HEARD GND TELL ME TO HOLD SHORT; I STOPPED IMMEDIATELY AND WAS NOT YET ON THE RWY IN QUESTION. HOWEVER; ONCE HE CLRED ME TO TAXI; I DID SO AND DID NOT CONTEST HIS STATEMENT THAT I WAS ON THE RWY ALREADY. I WOULD HAVE BEEN ON THAT RWY HAD THE GND CTLR NOT MADE HIS XMISSION. THE FO APPARENTLY HAD BEEN DISTR BY HIS COCKPIT DUTIES AND AS A FAIRLY NEW CREW MEMBER WAS NOT REAL FAMILIAR WITH THE ARPT; SO HE DID NOT NOTICE THAT A POTENTIAL RWY INCURSION WAS ABOUT TO OCCUR. THERE WAS NO CONFLICT THANKFULLY AND I HAD YET ANOTHER OPPORTUNITY TO GAIN EXPERIENCE AT A LOW PRICE! THE NORM HERE IS VIGILANCE AND COORD BY BOTH CREW MEMBERS. OR; MAKE THE RAMP AREAS AS STERILE AS THOSE OLD MIL FLT LINES AND I DOUBT WE'D EVER SEE THAT HAPPEN.