C90 CTLR EXPERIENCED CONFLICT AT APPROX 5000 WITH DEP ACFT WHEN ONE WAS NOT ASSIGNED CORRECT HEADING BY THE TWR.

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I WAS ASSIGNED THE S DEP POS. ORD WAS DEPARTING 32LT10/32R/4L/9R AND ARRIVING RWYS 9R/9L/4R. ACR X CHKED ON DEP; CLBING TO 5000 FT. ALL APPEARED NORMAL UNTIL I NOTICED ACR X WAS ON A NE HDG. WHEN I TOOK A CLOSER LOOK AT THE DEP STRIP; THE PRINTED ASSIGNED HDG WAS 070 DEGS. THERE WERE 2 OTHER DEPS WITHIN VERY CLOSE PROX. I KNOW THAT THERE WAS LESS THAN 3 MI; BUT I DON'T KNOW WHAT THE ALT SEPARATION WAS. IT VERY WELL COULD HAVE BEEN LESS THAN 1000 FT. I CLBED ACR X TO 6000 FT AND THEN 13000 FT AND TOPPED THE 2 OTHER DEPS. WHEN I ASKED ACR X TO VERIFY THE TWR ASSIGNED HDG; THEY SAID 040 DEGS. SO; NOT ONLY WAS THE DEP STRIP HDG WRONG; THE ACFT ASSIGNED HDG WAS WRONG AND SAFETY; IN MY OPINION; WAS ABSOLUTELY COMPROMISED. SOMETHING WENT VERY WRONG IN THIS SIT. I KNOW THE FAA WON'T DO ANYTHING ABOUT IT; SO I ADVISED ACR X THAT IN THE FUTURE; QUESTION WHAT DOESN'T SOUND RIGHT FOR YOUR RTE OF FLT. A NE HDG FOR A SWBOUND DEP IS WAY OFF. I THINK IT'S GOOD ADVICE TO ALL AVIATORS TO QUESTION WHAT DOESN'T SOUND RIGHT; IT COULD KEEP YOU SAFE!