I haven't called for my own cab at ORD for some time, but keep in mind that every taxi that arrives at the airport must go through a 'staging' area, and needs to be 'released' by the city in order to enter the airport pickup area. I'm 99.9% sure that includes 'ordered' cabs.

For that reason, if you're not willing to just take a cab that's already queued up, make sure that you call well in advance so that they know you're coming, and that you can make sure they'll have a cab ready to try and get out of the staging area as soon as you arrive. I've had problems before in which they've had trouble getting out.

The other solution, of course, is to just take a taxi from the cab stand.