Whatever it is the thing is beautifully made. I love the chrome and the way the wire hook elbow is brazed onto the clip portion. If it is as small as you are saying later in the thread it makes it all the more remarkable. It's not something from Kmart, THAT much is for sure. I bet it was expensive when new whatever it was for.
I vote for some sort of clipy framey hooky thingie. Is the circular portion springy steel or mild steel that stays bent when you move it?
It'd make a great necklace pendant or other jewelry do-dad in any case for the hipster/vintage velo artsy type -pretty/shiny!