NMAC BTWN A DC9-39 CLBING IN CLASS E AIRSPACE JUST OUTSIDE OF CLASS C AND BELOW CLASS B AIRSPACE; AND A GOV HELI DSNDING. THE GOV HELI ADVISED THAT THE DC9 WAS SIGHTED AND ATC INSTRUCTED PLT TO REMAIN CLR OF THE ASCENDING AND CONVERGING TFC.

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CAPT FLYING. DEPARTED OFF OF RWY 4 AT MDW WITH CLB TO 3000 FT AND INITIAL HDG (?). SWITCHED TO DEP AND WAS GIVEN A TURN TO 090 DEGS. CLBING THROUGH 1900 FT AND PASSING 070 DEG HDG; TCASII ALERT WITH 'MONITOR VERT SPD' CALLOUT. PWR HAD BEEN PULLED BACK BELOW CUTBACK EPR SINCE ONLY 1000 FT TO GO IN CLB AND CLBING AT APPROX 1500 FPM. PLANE CLBED TO 2100 FT. TCASII ALERT 'DSND; DSND' AS COPLT COMMENTED '300 FT ABOVE.' DSNDED TO 1900 FT AND CHKED TCASII FOR OTHER ACFT. I SAW CONVERGING ACFT SYMBOL PASS OVER ACFT. COPLT COMMENTED THAT HE 'DID NOT PICK UP THE OTHER ACFT VISUALLY.' HE SAW CONVERGING ACFT APPEAR ON TCASII SCREEN FROM 1-2 O'CLOCK POS. THE ALT OF OTHER ACFT CHANGED FROM 500 FT ABOVE TO 400/300/200 FT AND FINALLY 100 FT ABOVE OUR ACFT. ORD DEP WAS INFORMED OF THE RA AND NEAR MISS. THEY INFORMED ME THAT 'MDW TWR WAS CTLING THE OTHER ACFT AND THAT THE ACFT HAD US VISUALLY.' I SPOKE WITH MDW TWR SUPVR ON DUTY MAY/XA/98. HE INFORMED ME THAT THE CONVERGING TFC WAS A GOV HELI ON A SURVEILLANCE FLT. THE GOV HELI WAS SUPPOSED TO REMAIN CLR OF AN ASCENDING AND CONVERGING ACFT. THE MINIMUM VERT DISTANCE OF THE NEAR MISS; 100 FT; DEMONSTRATES THAT THIS WAS NOT POSSIBLE. IF THE PRIORITY OF AIR TFC WAS THE GOV SURVEILLANCE; THEN I SHOULD HAVE NOT BEEN CLRED FOR TKOF. IF DEP ACFT HAD THE PRIORITY CLRNC THEN THE HELI SHOULD HAVE BEEN GIVEN AN ALT ABOVE MY CLRNC ALT; 3000 FT. NEITHER THE ORD DEP NOR MDW TWR RECOGNIZED THE IMPENDING COLLISION AND NEITHER TOOK ACTION. IT IS IMPERATIVE THAT A REVIEW OF AIR TFC PRIORITIES IN REGARDS TO GOV SURVEILLANCE BE ACCOMPLISHED.