CL65 FLT CREW HAS A RWY INCURSION AT MDW.

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LANDED ON RWY 31C AT MDW AND TAXIED CLR OF RWY. TOLD TO TAXI TO AND HOLD SHORT OF RWY 22R AND SWITCH TO GND. CLRED BY GND CTLR TO CROSS RWY 22R ON TXWY N TO HOLD SHORT OF RWY 22L ON TXWY Q. READ BACK XING AND HOLD SHORT CLRNC. AS PER SOP'S; TURNED ON ALL AVAILABLE EXTERNAL LIGHTS; VISUALLY AND AURALLY CLRED L (APCH END OF RWY) AND R; AND STATED 'CLR R; CLR L; CLRED ACROSS RWY 22R.' I RELEASED PARKING BRAKE AND BEGAN TO TAXI ACROSS RWY 22R HOLD SHORT LINE. GND CTLR SPOKE OUR CALL SIGN WITH NO FURTHER INSTRUCTION; THEN HEARD AT LEAST 2 OTHER CTLRS IN THE BACKGND (EG; IN THE SAME ROOM) CALL 'STOP; STOP; JUST TELL HIM TO STOP.' THE GND CTLR THEN SAID 'HOLD POS.' I STOPPED THE ACFT AFTER HAVING CROSSED THE HOLD SHORT LINE. I LOOKED L AND SAW A BIZJET EMERGE FROM BEHIND A BUILDING WHICH IS TO THE R OF THE APCH END OF RWY 22R. HE APPEARED TO BE CONDUCTING A CIRCLE-TO-LAND VISUAL APCH. THE ACFT TOUCHED DOWN ON RWY 22R. GND CTLR THEN CLRED US ACROSS RWY 22R ON TXWY N TO HOLD SHORT OF RWY 22L ON TXWY Q. PROCEEDED RELATIVE TO GND CTLR CLRNC WITHOUT FURTHER INCIDENT.