ZAU Controller described a TCAS RA event between an IFR corporate jet that canceled IFR services leaving the frequency and an IFR air carrier; the Controller alleging all ATC requirements were completed per the 7110.65.

Narrative

I was working Aircraft Y [who was] coming from a high sector above me; while working the very narrow Harly sector; which serves as a departure route for southbound departures. Aircraft Y needed to land and was proceeding westbound. I cleared him to 14;000 FT; my lowest altitude limit. About a minute later; Approach launched a southbound departure; Air Carrier X; climbing to 13;000 FT; which put the aircraft in direct conflict with Aircraft Y. My next control instruction was; 'Aircraft Y; amend altitude; maintain 16;000 FT; turn 30 degrees right; RADAR vectors traffic.' Aircraft Y refused to comply as he broke through 17;900 FT when I told him the clearance. He told me he wanted to cancel services with ATC. I took this to be kind of strange; because I just told him to turn for traffic. Why would he want to cancel ATC services and put his life as well as others at risk? I quickly responded; 'Aircraft Y; you want to cancel?;' and he responded as; 'Yup; we're out of here;' sarcastically and left the frequency. After that; I followed the 7110.65; used proper phraseology and told him; 'Aircraft Y; RADAR services terminated; squawk 1200; cleared from Center frequency.' I got no response from aircraft Y. Immediately after that; Air Carrier X checked on; climbing to 13;000 FT; and had no idea about the VFR traffic out there. I told him to climb and maintain FL230 and be advised there is fast moving VFR traffic at 10 o'clock descending fast in a westbound direction. I continued to make about 3 traffic calls to my only IFR traffic. Aircraft Y; now just a 'V' on my RADAR display; was descending so fast it was hard to determine if he was going to pass over or below Air Carrier X. The two targets got close and Air Carrier X told me he was responding to an RA and descending back down to 13;000 FT; as the 'V' passed right behind him. About 30 seconds later; Air Carrier X told me; 'I never saw him.' This was really close; I don't recall ever having two targets pass so close to each other at the same altitude. I immediately informed the Supervisor that one of my aircraft had an RA at my sector and filled out the appropriate paperwork. In my opinion; I did nothing wrong.