Is it possible to add a pixel above chrome tabs?

Question

Google Chrome

A common action is to drag the browser window to the second monitor.
In opera above the tabs in full screen mode, there is little of the window title bar so it's easy to feel for.
And in chrome, tabs stick to the border of the screen, so you need to hover over the free space, which, with several open tabs, will be several pixels in size from the edge.
Is there a solution?