B737-300 FLT CREW ENCOUNTERS SEVERE TURB WHILE ENRTE.

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ON THE WAY TO MDW; WE WERE DEVIATING AROUND LEVEL 3 AND 4 TSTMS. WE ASKED THE FLT ATTENDANTS TO REMAIN SEATED. WE WERE IN MODERATE TURB FOR SEVERAL MINS. WE THEN EXPERIENCED SEVERE TURB FOR 3-5 MINS. AFTER THAT WE WERE BACK INTO MODERATE TURB. THIS LASTED ALMOST THE DURATION OF THE FLT. ON THE APCH TO MDW I CALLED IN-RANGE TO HAVE MAINT MEET THE ACFT UPON ARR DUE TO THE FACT THAT WE WERE IN SEVERE TURB. THE FLT ATTENDANTS REMAINED SEATED FOR THE REST OF THE FLT. WE HAD TO SHOOT AN ILS RWY 31C CIRCLE-TO-LAND RWY 22L. DURING THE SEVERE TURB WE HAD +/- 50 KTS AND THE IVSI WAS +/-2000 FT. THE ACFT WAS AT MINIMUM CTL. UPON ARR TO MDW; MAINT MET US AT THE GATE. WE DISCUSSED WHAT HAD HAPPENED WITH THEM. OUR FLT ATTENDANTS WERE NOT HURT. WE TALKED TO THEM AND THEY WERE SHAKEN UP AS ANYONE WOULD HAVE BEEN. WE HAD 1 MORE LEG SO WE HAD TO CATCH ANOTHER AIRPLANE AT ANOTHER GATE. DURING THIS FLT; WE NEGLECTED TO CONTACT DISPATCH. I FEEL THAT WE WERE TASK SATURATED. THERE WERE NO PIREPS OF SEVERE TURB IN THAT AREA. WE DID NOT EXPECT TO ENCOUNTER THIS. NONE OF THE PAX WERE HURT. WE DID NOT FLY INTO ANYTHING WORSE THAN LEVEL 2 ACCORDING TO THE RADAR. I AM NOT SURE HOW WE COULD HAVE AVOIDED THIS. SUPPLEMENTAL INFO FROM ACN 690243: THE TURB GOT SO BAD THAT THE AIRSPD VARIED ABOUT 80 KIAS. WE CONSTANTLY BATTLED UNCOMMANDED 30+ DEG ROLLS; AND THE ACFT WAS CONSTANTLY CLBING AND DSNDING SEVERAL HUNDRED FT.