CORPORATE C550 PLT ON DEP HAS NMAC WITH A HAWKER ON VISUAL APCH.

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CLRED FOR TKOF RWY 27 (DPA) WITH CLRNC TO TURN L TO A HDG OF 160 DEGS AND 3000 FT. A HAWKER HAD BEEN CLRED FOR A VISUAL APCH TO RWY 1L AND WAS ENTERING A DOWNWIND (L) AS WE WERE CLBING OUT. AS I WAS IN THE L TURN; CLBING THROUGH APPROX 1600 FT MSL; TWR ASKED IF WE HAD THE HAWKER. THIS WAS THE FIRST COM WITH US ABOUT THIS ACFT. THE R WING OF OUR ACFT WAS RAISED AND PREVENTED ME FROM SEEING THE TFC. THE PNF THEN SAW THE TFC AND TOLD ME TO KEEP BANKING HARD L. WHEN I DID GET HIM IN SIGHT A MOMENT LATER; I WAS SURPRISED TO SEE HIM SO CLOSE AND REDUCED PWR AND BEGAN A DSCNT. WHEN WE WERE CLR I RESUMED THE CLB. WE HAD A VERY GOOD LOOK AT THEIR BELLY! WE UNDERSTAND THAT HUMAN ERROR OCCURS AND DO NOT FEEL COMPELLED TO MAKE AN ISSUE OF THIS WITH THE TWR. THE CTLR REALIZED HIS ERROR AND WILL PROBABLY SELF-EVALUATE. I THINK HE HAS A RPT TO SUBMIT FOR NEAR MISSES TOO?! I DO HOPE TO GET A COPY OF THE AUDIO TAPE TO REVIEW WITH MY FLT DEPT. WE (THE CREW) HAVE DISCUSSED WAYS IN WHICH WE COULD HAVE PLAYED A ROLE IN PREVENTING THIS OCCURRENCE. SITUATIONAL AWARENESS COMES TO MIND. WE VOW TO LISTEN CLOSER TO OTHER ACFT XMISSIONS TO ENSURE THAT WE DON'T GET A CLRNC TO OCCUPY THE SAME AIRSPACE AT THE SAME TIME.