AIR TAXI PLT CROSSES RWY HE WAS CLRED TO HOLD SHORT.

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MY ACFT TAXIED ACROSS AN ACTIVE RWY 22L/4R. RWY 31C WAS THE MAIN ACTIVE AT THE TIME AND I HAD JUST LANDED ON 31C. DEPARTING; I READ BACK MY TAXI CLRNC WITH THE HOLD SHORT INSTRUCTION OF 'HOLD SHORT 22L.' I TAXIED AS TOLD ON E/W TAXIWAY TO F AND TO HOLD SHORT OF 22L. A PAX OCCUPIED THE COPLT SEAT AND WAS ASKING ME QUESTIONS. GND CTL WAS BUSY AND I COULD NOT GET THROUGH TO ASK FOR PROGRESSIVE TAXI INSTRUCTIONS. I DID NOT REALIZE I HAD CROSSED 22R AND WAS APCHING 22L. THE RWY WAS MARKED 4R. AS I PARTIALLY ENCROACHED ON 22L/4R; I REALIZED MY POS AND CONTINUED TO CROSS AS I HAD ALREADY LOOKED FOR TFC ON OR APCHING THE RWY. TFC WAS STILL USING 31C; BUT 22L WAS ALSO ACTIVE. I WAS IN ERROR; BUT NO CONFLICT WAS APPARENT. THE RWY AND TAXI MARKINGS AT MIDWAY NEED IMPROVEMENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES HE WAS AT MDW SINCE INCIDENT AND DOES BELIEVE SIGNS SHOULD BE IMPROVED TO INDICATE BOTH RWY DESIGNATIONS. GRANTED HE SHOULD KNOW 4R OPPOSITE END IS 22L; BUT WHEN TAXIING AND RUNNING CHKLISTS; ONE IS SO BUSY HE JUST ACCEPTS WHAT SIGN INDICATES. HE ALSO HAD A COMPANY ACFT RIGHT BEHIND; A FLT OF 2; AND DID NOT WANT TO SLAM ON THE BRAKES AND GET CHEWED UP. NO TFC ON 22L AT THE TIME.