Moving away from the window to another window gets it out of this state.

(Also, if this helps, my desktop environment is XFCE.)

Can't seem to repro on Cinnamon/Muffin.  I'll set up XFCE in a VM to see if there's any difference.

How long does it take to get into this state?  Maybe you can try to bisect-builds?

Moving away from the window doesn't always get it out of this state, specifically, I need to switch to a window which would cover the broken chrome window to get out of it.

It may also need to have the window fully covered to get into this state (or it may not; still needs more testing).

I'm getting into this state every 10 minutes or so?

This might just be weirdness with my machine? I got a driver update the other day, and I'm suspecting that might be it. I can reproduce this going back to 52.0.2719 / 2fd6ac7 under xfce (I didn't try to go back further.)

I'm going to try to live in Unity for a few days and see if it replicates there.

Weird, I just got a driver update too (367.35), and things are now broken on Cinnamon (dragging windows is really slow for all windows), but not seeing the redraw issue.  Unity is fine though.  

I can confirm that things mostly work on Unity on my machine.

Happens to me too on XFCE.  Perhaps this is a dup of  http://crbug.com/638090 ?

 Issue 638090  has been merged into this issue.

I was finally able to repro on xfce on the unstable channel

A reliable repro: (not sure if every condition is necessary)
Maximize chrome.
Focus an app on top of chrome.
Wait about 10s.
Move the cursor over the chrome window and scroll.
Chrome will get focus and will be raised, but will not redraw.