I've heard the horror stories about customer service, needed mechanical repairs, and faulty bracelets, but yours was the very first one involving paint chips. But there may be some reality to this story. Are these other Bolt Zeus owners referring to the paint chipping off the decorative cable pieces used on the watch?
This is a screen shot of a Zeus I found over at Amazon. When I enlarged the photo, I noticed a couple very small white spots on the cable surrounding the case but assumed it was nothing more than reflected lighting. Then I happened to notice the bracelet.
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Those aren't reflections.
My two cents: (1) Send it back in exchange for an unpainted model (2) Keep the watch, and have handy a small bottle of modeling kit enamel for touch-ups (3) Just send it back and wait for the next new model that catches your eye. And that shouldn't be long. It seems like every other month Invicta introduces a brand new model.