Are you sure? Cites this time:
California: The driver of a vehicle intending to turn to the left or to complete a U-turn upon a highway, or to turn left into public or private property, or an alley, shall yield the right-of-way to all vehicles approaching from the opposite direction which are close enough to constitute a hazard at any time during the turning movement, and shall continue to yield the right-of-way to the approaching vehicles until the left turn or U-turn can be made with reasonable safety.
Not crystal clear, I admit, but in other states it seems to be:
New York: If drivers approaching from opposite directions reach an intersection at about the same time, a driver turning left must yield to approaching traffic going straight or turning right.
Ohio: Right Of Way When Turning Left - The driver of a vehicle attempting to turn left shall yield the right of way to a vehicle approaching from the opposite direction.
Tennesee: When turning left at intersections you must yield to any oncoming vehicle proceeding straight or turning right, unless you have a traffic light where your left turn is on a protected green arrow.
Now, of course, if the intersection has a light specifically for left-hand turns (or U-turns, to reference the OP) then the light trumps anything else. But the OP implies that he was waiting far “a gap in traffic,” by which I assume that he wasn’t at a green arrow. In which case he’s supposed to follow whatever the default right-of-way law (in Illinois, I assume). Which I don’t know what it is, but if I were forced to guess, I’d think the right-turner has the right-of-way, based on the following:
Illinois: 625 ILCS 5/11-902)
Sec. 11-902. Vehicle turning left. The driver of a vehicle intending to turn to the left within an intersection or into an alley, private road, or driveway shall yield the right-of-way to any vehicle approaching from the opposite direction which is so close as to constitute an immediate hazard, but said driver, having so yielded may proceed at such time as a safe interval occurs. (Source: P.A. 76-1586.)
Of course, I’d prefer if Freejooky clarified the situation.