AN AIR TAXI JET EXPERIENCES A RWY INCURSION AT MDW; IL.

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WE TAXIED OUT FROM RAMP AT KMDW. OUR INSTRUCTIONS WERE TO TAXI TO RWY 22R. I INQUIRED WITH GND CTL ABOUT XING RWYS 13L; R AND L. WE WERE CLEARED TO DO SO. AFTER XING RWY 13L; I WAS IN THE PROCESS OF TRYING TO COMPLETE THE TAXI CHECKLIST AND ASSOCIATED ITEMS. THE CAPT WAS TAXIING EXCESSIVELY FAST AND I FELT RUSHED TO COMPLETE THE CHECKLIST IN TIME. THE CAPT THEN RECEIVED A MESSAGE FROM COMPANY; VIA COMPANY ISSUED PAGERS; WHICH HE PROCEEDED TO LOOK AT WHILE TAXIING. I HAD MY HEAD DOWN DOING THE CHECKLIST ITEMS WHEN WE CROSSED OUR ASSIGNED RWY 22R. WE WERE NOTIFIED BY GND CTL AT THAT POINT THAT WE HAD CROSSED OUR RWY. WE PROCEEDED TO CONTACT TWR AND EVENTUALLY DEPARTED ON RWY 22L. CORRECTIVE ACTION: THE CAPT SHOULD HAVE BEEN TAXIING SLOWER AND HE SHOULD HAVE WAITED TO RETRIEVE THE COMPANY MESSAGE UNTIL WE WERE STOPPED AT OUR RWY. I SHOULD HAVE BEEN IN A MORE HEADS-UP MODE AND AS WE NEARED OUR RWY I SHOULD HAVE HALTED MY EFFORT AT COMPLETING THE TAXI CHECKLIST. THIS WAS OUR FIRST LEG TOGETHER AS A CREW.