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(This is a reland of r283813 which was reverted in r283845 because it broke
WebRTC tests on Android. That, in turn, was a reland of of r283542 which was
reverted in r283591 because it broke the WebView build.)

This is a much larger change than its diff suggests. If it breaks
something, please revert first and ask questions later.

BUG=none

Review URL: https://codereview.chromium.org/401613008

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@284079 0039d316-1c4b-4281-b951-d872f2087c98