COMPUTER LTT HAS NMAC WITH SMA ON DEP; AT 1000 FT.

Narrative

WE WERE DEPARTING CHICAGO MIDWAY. WE WERE DEPARTING RWY 31C; USING THE MIDWAY 4 DEP. AT 1000 FT MSL THE CAPT AND I BOTH SAW A HIGH WING SINGLE ENG CESSNA AT ABOUT 150 FT SLIGHTLY HIGH; PASSING FROM L TO R; THE ACFT APPEARED TO BE FOLLOWING THE HWY BELOW. I IMMEDIATELY PUSHED FORWARD ON THE CTLS TO ARREST MY ASCENT TO AVOID COLLISION. AFTER CLRING THE ACFT I CONTINUED MY CLB AND STARTED A TURN TO 100 DEGS AS PER THE MDW 4 DEP AND MAINTAINED VISUAL SEPARATION. AFTER BEING HANDED OFF TO DEP; WE RPTED THE INCIDENT; THE CTLR WAS SUPPOSED TO 'PASS IT ALONG.' BEFORE TKOF I RECALL HEARING TWR TALKING WITH A CESSNA WHO SOUNDED DISORIENTED WITH RESPECT WITH HIS POS IN RELATION TO THE ARPT; AND WAS WAITING TO PASS THROUGH (I BELIEVE ENRTE TO MAJOR FIELD). I FEEL THAT THE ACFT MAY BE THE ONE WE ALMOST HIT. ATC WAS OBVIOUSLY UNAWARE OF THE TFC AT THE DEP END OF RWY 31C. ATC FOR MDW IS USUALLY TOPS BUT SOMEONE 'DROPPED THE BALL' ON THIS ONE WAS THE WORDS OF THE FAA INSPECTOR SITTING IN THE JUMPSEAT.