Alright, I can see the case where someone doesn't habitually close it and stumbles upon a site where it is obscuring. It seems rather mild to me, but I guess I could regard that as a UX failing.
The only solutions that immediately come to mind:
A) Place the "Find on Page" box at the bottom of the window.
Advantages: It would get out of the way for the common practice of placing web UI at the top of the viewing pane. Also the tradition of putting other UI elements at the bottom (namely the download bar comes to mind) means that it wouldn't be too unfamiliar.
Drawbacks: This _would_ put it rather far from it's omnibox UI-sibling and the rest of the prefs UI, breaking some of the association for the UX. It doesn't resolve the problem of UI elements being obscured the bottom of the viewing pane.
Seen also in: I know at least Firefox does this.
B) Have the "Find on Page" UI element displace the page so as to not cover any page UI while "active"
Advantages: Won't cover UI. Potentially more room for search terms.
Drawbacks: Takes up more screen real estate.
Seen also in: I know at least Firefox does this as well.
Alright, so those are potential solutions... what I'm more interested in are the ones I _haven't_ thought of. Does anyone in the HN community have a brilliant solution for how to deal with designing a "Find on Page" UI?