For some unfathomable reason the SketchUp coders think this keychain thing is a good idea, it was never there before Google bought them out.

The way I got rid of it was to run the KeyChain Access application in the Utilities folder and look for the 3 SketchUp items in the login keychain. Then double clck on each and change the access control from "confirm before allowing access" to "allow all appllications to access this item". That then gets rid of the prompt.

Of course it makes the items less secure (though I've no idea what these things are trying to store anyway), but short of being able to remove this thing entirely it beats being prompted for 3 passwords every time you launch the application.