Selected div appears with a border on selected on chrome and safari
Try adding this in your CSS:
*:focus { outline: none;}
That should get rid of the focus highlight for the whole page.
I know this is old, but for reference for others is that the div becomes selectable in Chrome once the tabIndex property is added. a trick was used to make the tabIndex negative for elements that could not be tabbed to but even then the select rectangle was shown.