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Probably a nail in the tire...Raise that wheel and inspect thoroughly.
This can often happen with no loss of air pressure if the nail is in there Just right..
Check for codes and make sure none are set for ABS. Jack it up and give the tire a good shake (up and down and side to side}. Pull the tire and wheel. Inspect tire tread, make sure lug nuts were tight, look over the hub and brake assembly (should be tight and turn without noise), check all the end links (sways, steering, etc). Something is probably loose.
I haven't had a chance to look the car over, but I wanted to add that I can now hear it going straight too. When I'm close to a curb or if there's a car next to me, I can really hear the noise because it will bounce off. The faster I go, the faster the clicking is.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.