MD80 CREW DSNDING INTO ORD RECEIVED A TCAS RA TO AVOID VFR ACFT ALSO IN CONTACT WITH ARTCC.

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WE WERE GIVEN A CLRNC TO PROCEED DIRECT TO ORD WHILE DEVIATING AROUND TSTMS TO THE SW OF CHICAGO. WHILE DIRECT TO ORD AND IN A DSCNT WE WERE INSTRUCTED TO DSND TO 11000 FT. I NOTICED THAT THIS CLRNC WOULD TAKE US THROUGH AN AREA OF ALTOCUMULUS CLOUDS WITH RAGGED TOPS UP TO APPROX FL180. I CALLED THE FLT ATTENDANTS AND INSTRUCTED THEM TO TAKE THEIR JUMPSEATS AS I EXPECTED THE RIDE TO BE ROUGH WHEN WE ENTERED THE CLOUDS. THIS WAS FORTUITOUS AS ALL THE FLT ATTENDANTS WERE SEATED WHEN WE RECEIVED AN RA A SHORT TIME LATER. I DEPLOYED THE SPD BRAKES TO EXPEDITE OUR DSCNT THROUGH THE AREA OF CUMULUS CLOUDS SO AS TO MINIMIZE THE TIME WE WOULD BE EXPOSED TO THE ROUGH RIDE. ABOUT THIS TIME THE CTLR ALSO INSTRUCTED US TO DSND AT LEAST AT A RATE OF 2500 FPM. AS WE STARTED TO ENTER THE VICINITY OF THE CLOUD BANK; WE WERE GIVEN A TURN TO A HDG OF 360 DEGS. JUST AS WE ROLLED OUT ON A HDG OF 360 DEGS; SOMEWHERE BELOW FL180; THE TCAS SYS ISSUED A TA. I LOOKED AT THE TCAS DISPLAY TO SEE A CONFLICT ACFT SLIGHTLY TO OUR L AND WELL WITHIN THE 2 MI CIRCLE OF THE TCAS DISPLAY. THIS ACFT WAS INDICATING AN ALT APPROX 2000 FT BELOW OURS. WITH THIS; I RETRACTED THE SPD BRAKE; DISCONNECTED THE AUTOPLT AND BEGAN TO ARREST OUR DSCNT BY RAISING THE NOSE. I ALSO BEGAN A SHALLOW R TURN AWAY FROM THE OTHER ACFT. A MOMENT LATER; WHILE DSNDING THROUGH APPROX 14000 FT WE RECEIVED AN RA WITH A 'MONITOR VERT SPD' AURAL WARNING. THE CONFLICT ACFT WAS NOW MERGED WITH OUR OWN ACFT SYMBOL ON THE TCAS DISPLAY AND WAS NOW SHOWING A CLB AND AN ALT OF APPROX 1000 FT BELOW OUR OWN ALT AND CLOSING FAST AS WE CONTINUED TO DSND. I LOOKED AT THE VSI TO SEE A CLB INDICATION AND RESPONDED ACCORDINGLY WHILE CONTINUING THE SHALLOW R TURN. THIS WAS VERY QUICKLY FOLLOWED BY AN 'INCREASE CLB' COMMAND. WHEN I AGAIN LOOKED AT THE VSI IT WAS COMMANDING A CLB OF 2000 FPM OR GREATER. WE EVENTUALLY REACHED A DECK ANGLE OF 20 DEGS OR PERHAPS A LITTLE GREATER AS I RESPONDED TO THE COMMAND AND CLBED TO 17000 FT. AT THIS POINT; TCAS INDICATED CLR OF CONFLICT. DURING THIS FAST PACED EVENT THE FO DID AN EXCELLENT JOB. HE RPTED OUR RESPONSE TO THE RA TO ATC; BACKED ME UP ON MY RESPONSE TO THE TCAS COMMANDS; AND KEPT ME INFORMED OF THE OTHER ACFT'S RELATIVE POS. I AM DISAPPOINTED TO RPT THAT AT NO TIME DID ATC ISSUE A TA OR ATTEMPT TO VECTOR US AROUND THE CONFLICT ACFT. THE FO FELT THAT THE OTHER ACFT WAS A PARACHUTE JUMP ACFT THAT WAS IN CONTACT WITH ATC. HE STATED HE HEARD THE CTLR SAY TO THE OTHER ACFT THAT HE; THE CTLR; THOUGHT THE PLT OF THE OTHER ACFT SAID HE WAS DSNDING NOT CLBING. I NEVER SAW THE OTHER ACFT EVEN THOUGH WE WERE VIRTUALLY ON TOP OF HIM AND I BELIEVE HE WAS IN THE CLOUDS JUST BELOW US THAT WE WERE ABOUT TO ENTER JUST AS I STARTED THE CLBING RESPONSE TO THE TCAS COMMAND. IF THIS WAS A PARACHUTE JUMP PLANE IT IS LIKELY HE WAS OPERATING UNDER VFR AND I DON'T BELIEVE IT WAS POSSIBLE FOR HIM TO BE IN COMPLIANCE WITH VFR CLOUD CLRNCS.