I've gotten my pimento wood shipped from a distributor in Minnesota of all places. In fact, I have two sticks under the coffeetable at this moment.
http://www.pimentowood.com
It ain't exactly cheap for what you get. The sticks are about 12 inches long and about an inch in diameter. It's $30 for four. Supposedly, they can be reused, but the last time I jerked a chicken, I used two sticks--I probably would have gone all four if they weren't $30.
Now, the wood chips are $15 for 90 cubic inches. I can't conceptualize how much wood that actually is, but the website claims it's good for 10-12 smoking sessions. I've never bought them.
edit: I suspect this must be the "place on the internet" you're talking about. As far as I know, there's no place in Chicago that sells pimento wood. Now, one lead I've never followed up on is Calypso Cafe in Hyde Park. When I was last there, the waitress claimed that the jerk chicken was indeed smoked/grilled over pimento wood, although she said I would have to come back the next day to talk to the person in charge of buying it to ask where it comes from. She was good enough to bring a sample from the kitchen, but they were wood chips and I could not tell by looking at them whether they were in fact pimento or not. But it's a long shot you can try.