DA42 INADVERTENTLY PENETRATED CLASS B AIRSPACE DURING INSTRUCTIONAL FLT.

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DEPARTED XA30 FROM UGN (CLASS D CTLED) IN DA42 TWINSTAR WITH STUDENT WHO IS A CERTIFICATED ATP/MEL; SEL CFI AND CFII. I WAS PROVIDING MEI DUAL INSTRUCTION AND PREPARING STUDENT FOR MEI P61 FLT TEST. STUDENT WAS QUALIFIED AND CURRENT TO ACT AS PIC IN DA42. I ASKED STUDENT PRIOR TO ENTERING ACFT IF HE HAD CURRENT TERMINAL AREA CHARTS FOR CHICAGO AREA AND IF HE WAS FAMILIAR WITH CLASS B AIRSPACE SHELVES SINCE THE UGN ARPT WAS LOCATED UNDERNEATH THE ORD CLASS B. STUDENT HAD A CURRENT CHART AND WAS FAMILIAR WITH SURROUNDING AREA AND AIRSPACE. FURTHERMORE; STUDENT INDICATED HE WAS PROVIDING SEL DUAL INSTRUCTION DAILY FROM THE UGN ARPT. DURING PRE TKOF BRIEFING; STUDENT INDICATED HE WAS ACTING PIC AND CONTINUED THROUGH TRADITIONAL MEL PRE TKOF BRIEFING. STUDENT HELD SHORT OF RWY 23 AND REQUESTED NE DEP; CLRNC WAS GRANTED AND WE DEPARTED VFR FROM RWY 23. STUDENT BEGAN L TURNOUT TO GENERAL EASTERLY DIRECTION. SHORTLY AFTER; I WAS DISTR WITH OTHER DUTIES INCLUDING REACHING BEHIND SEAT TO PROCURE EMER CHKLISTS FOR MULTI-ENG/SINGLE-ENG TRAINING AND FAILURE; IFR CHARTS AND APCH PLATES. DA42 IS EQUIPPED WITH GARMIN G1000 AND AFTER REFING PFD; I NOTICED STUDENT WAS IN AN AGGRESSIVE CLB AT VY. AT THAT TIME I ALSO NOTICED ACFT WAS IN A SE HDG AND PASSING THROUGH 4000 FT MSL. SINCE THE STUDENT WAS FLYING A SE HDG INSTEAD OF FULLY COMPLETING THE L TURN TO THE NE AS ORIGINALLY REQUESTED; WE WERE NOW INADVERTENTLY INSIDE THE ORD CLASS B OUTER RING AS DEPICTED ON THE G1000 MFD. WE WERE LOCATED APPROX 9 DME FROM THE OBK VOR ON THE 050 DEG RADIAL. AFTER REFING THE CHART AND CONFIRMING THE OUTER RING WAS FROM 3600-10000 FT MSL; I TOOK CTL OF ACFT; LEVELED AT 4500 FT MSL; AND INITIATED AN IMMEDIATE DSNDING L TURN TO A HDG OF 360 DEGS TAKING US DIRECTLY OUT OF THE AIRSPACE. APPROX 3 MI LATER; THE ACFT WAS CLR OF THE CLASS B AIRSPACE. DURING THAT TIME THERE WAS NO TFC VISUALLY IN THE AREA OR ON THE ACFT'S TIS. THE ACFT'S MODE S XPONDER WAS ACTIVELY SQUAWKING AND SET TO 'ALT.' IN REFLECTION OF THE INCIDENT; IT WAS CLR THE STUDENT MAY HAVE BEEN A HIGHLY CERTIFICATED PLT AND INSTRUCTOR THAT FLEW IN THAT AREA DAILY. HOWEVER; HE WAS OUT OF HIS ELEMENT IN A MORE COMPLEX MULTI-ENG ACFT AND WAS ACTING AS A STUDENT INSTEAD OF HIS TRADITIONAL INSTRUCTOR ROLE. I TOOK INTO CONSIDERATION HIS EXPERIENCE AND NEGLECTED TO CLOSELY MONITOR HIS ACTIVITIES AS I WOULD WITH A PRIMARY STUDENT. IN THE FUTURE; I WILL NOT MAKE ASSUMPTIONS BASED ON CERTIFICATION LEVELS AND EXPERIENCE; BUT CLOSELY MONITOR ACTIVITIES OF ANY STUDENT. I COULD HAVE ALSO BEEN BETTER PREPARED PRIOR TO TAKEOFF AND HAD ALL OF THE NECESSARY CHARTS AND CHKLISTS SITUATED ACCORDINGLY SO I WAS NOT DISTR DURING A CRITICAL PHASE OF FLT. TO PREVENT THIS SIT IN THE FUTURE; I INTEND TO UTILIZE MORE EFFECTIVE CRM AND PREFLT PLANNING PRACTICES. I ALSO MONITORED GUARD 121.5 WHILE OPERATING INADVERTENTLY IN THE CLASS B DURING THESE 2-3 MINS AND WHILE OUTSIDE THE AIRSPACE FOR THE REMAINDER OF THE FLT. IN RETROSPECT; IT MAY HAVE BEEN MORE APPROPRIATE TO CONTACT ORD APCH AND ADVISE THEM OF THE INADVERTENT INCURSION AND REQUEST A SQUAWK CODE AND CLRNC WHILE EXITING THE AIRSPACE.