AN ACR JET TAXIES ACROSS RWY 31R AT MDW WHEN HE WAS TOLD TO HOLD SHORT OF THAT RWY ON THE WAY TO RWY 31C.

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TAXIED FROM GATE AT MDW TO RWY 31C. AFTER XING RWY 31R ENRTE TO RWY; CTLR SAID WE WERE TOLD TO HOLD SHORT OF RWY 31R. LUCKILY; THERE WAS NOT A CONFLICT -- COULD HAVE BEEN A DISASTER. CHAIN OF EVENTS: 1) THE APU WAS INOP; SO #1 ENG WAS STARTED AT GATE. THE #2 ENG COULD NOT BE STARTED AT THE GATE (I THINK IT'S AN ARPT RULE HAVING TO DO WITH JETBLAST IN THE VERY SMALL ALLEYWAY BTWN CONCOURSES). THIS INCREASED OUR WORKLOAD BECAUSE OF ABNORMAL CHKLISTS AND COORDINATING WITH GND CTL TO FIND A SPOT TO XBLEED START THE #2 ENG. 2) WE HAD ARRIVED LATE IN MDW; SO THE TURN TIME WAS VERY FAST AND WE WERE RUSHED IN OUR PREPARATION FOR THE NEXT TKOF. I COULD SENSE THAT THE FO FELT PRESSURED; SO I SLOWED THE TAXI SPD AND GAVE HIM PLENTY OF TIME TO DO THE UNUSUAL CHKLISTS. 3) I DON'T FLY TO MDW VERY OFTEN; SO IT'S DIFFICULT TO TAXI THERE AT NIGHT. IT'S EASY TO GET CONFUSED THERE BECAUSE SO MANY OF THE TXWYS AND RWYS INTERSECT AT ODD ANGLES. KEEPING THAT IN MIND; I ACTUALLY WROTE THE TAXI CLRNC ON MY CLIPBOARD; BUT I DIDN'T WRITE DOWN TO HOLD SHORT OF RWY 31R. 4) SO I TAXIED ACROSS RWY 31R THINKING I WAS NOT REQUIRED TO STOP. 5) AFTER GND TOLD US OF THE MISTAKE; THE FO SAID HE DIDN'T KNOW WE HAD CROSSED RWY 31R. HE WAS EITHER PREOCCUPIED OR DIDN'T KNOW WHERE WE WERE ON THE ARPT (OR BOTH). HE DID KNOW THAT WE WERE SUPPOSED TO HOLD SHORT. THE ONE THING I PROBABLY COULD HAVE DONE WOULD BE TO QUIZ THE FO OR GND CTL BEFORE XING THE RWY. I DIDN'T DO THAT BECAUSE I HAD THE TAXI INSTRUCTIONS WRITTEN DOWN (OBVIOUSLY WRONG). IT WOULD HAVE HELPED TO HAVE A THIRD CREW MEMBER (FE) TO RUN THE ABNORMAL CHKLIST. BUT I WILL NEVER HAVE THAT LUXURY AGAIN BECAUSE THE FAA THINKS 2 PLTS ARE AS SAFE AS 3.