A320 DISPATCHED TO ORD WITH NO ALTERNATE OR HOLD FUEL ENCOUNTERS UNFORECAST CONVECTIVE WX. MICROBURSTS AND LNDG VISIBILITY OBSCURED BY HEAVY RAIN. DIVERT TO MDW; LNDG WITH MINIMAL FUEL IN CONTINUED INCLEMENT WX.

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WX BRIEF AND FLT PLANNING NORMAL. DISPATCH AND WX BRIEF MSG BOTH INDICATED NO TSTMS AT TIME OF ARR. WE DID NOT CARRY GAS FOR ALTERNATE PER SOP. UPON ARR IN ORD; TSTMS WERE BUILDING RAPIDLY AND MANY PLTS BENEATH WX WERE RPTING DOWNSHAFTS AS THEY BEGAN. DSCNT AND APCH TO RWY 14R WAS SMOOTH WITH SOME TS AVOIDANCE. AT MARKER; FLT IN FRONT OF US WENT THROUGH A CELL THAT WE CHOSE TO GO AROUND. APCH AND WINDS WERE STABLE THROUGHOUT FLARE. ORD CALLED WINDS AT APCH AND MIDFIELD AND THEY WERE STEADY AND WITHIN LIMITS. NO PWS INDICATIONS FROM JET. WE COULD SEE A RAINSHAFT AT APCH END OF RWY 14R AND WITH WIND RPT FROM TOWER FELT IT OKAY TO CONTINUE. THEY HAD MICROBURST ACTIVITY AT THE ARPT BUT DID NOT SPECIFY OUR RWY. ACFT IN FRONT OF US DID NOT GIVE A PIREP. IN FLARE; RAIN INTENSITY PREVENTED ADEQUATE VISIBILITY AND AT 30 FT EXECUTED A GAR. ON THRUST REDUCTION AT 4000 FT LEVEL OFF; ENG #2 HAD ONE STALL BANG. WE DECLARED MIN FUEL AND NEEDED TO FIND A PLACE TO LAND. ORD SHUT DOWN ARRS SO WE ELECTED MDW. DISPATCH NOTIFIED AND WE WENT TO A VISUAL RWY 22L WITH MIN FUEL LNDG UNEVENTFUL.SUPPLEMENTAL INFO FROM ACN 743529: RAIN SHOWER VISIBLE NEAR RWY 14R THRESHOLD. DISCUSSED WINDSHEAR RECOVERY MANEUVER AND MISSED APCH PROCEDURE. CONTINUED VERY STABLE APCH. WIND CHECK AT 500 FT REVEALED STABLE WIND COMPARED TO US AND RWY. APCH VERY STABLE TO 50 FT AGL WHEN WE WENT AROUND DUE TO MODERATE RAIN AND REDUCED VISIBILITY. NO AIRBORNE OR GND WINDSHEAR WARNINGS. TOWER ISSUED HEADING 090 DEGS AND 4000 FT. LEVELING AT 4000 FT NUMBER 2 ENGINE COMPRESSOR STALLED AT POWER REDUCTION. FUEL NOW ABOUT 4200 LBS. DECLARED MIN FUEL AND TOWER ASKED IF WE WERE OK. THEY HEARD WE HAD AN POSSIBLE ENGINE PROBLEM. WE ADVISED COMPRESSOR STALL. QUICKLY ASSESSED ENGINE AND WERE HANDED OFF TO APCH. DECLARED AGAIN MIN FUEL TO APCH AND GIVEN CLIMB TO 13000 FT AND ASKED WHAT OUR ALTERNATE WAS. I ADVISED WE WERE LOOKING. FINALLY GOT COCKPIT SPLIT. FO FLEW AND TALKED. I LOOKED AT WX AND DISTANCE 78 MILES AND MIDWAY. FUEL NOW ABOUT 4.0. NOTIFIED DISPATCH WE WERE GOING TO MDW. THEY AGREED. WHEN SWITCHED TO APCH FOR MIDWAY AND HEARD AN ACFT GOING AROUND. THINKING ABOUT GARY; IND; NOW. WINDS AT MDW 270/23. VISUAL APCH RWY 22L WITH LNDG FUEL NOW AT 3200 LBS. THROAT A LITTLE PARCHED.