Reland of https://chromium-review.googlesource.com/c/591667/, removing thread-local variable

Bug: 
Change-Id: Ia9bc73be4a46a6bf052220726193c8b6634eb73e
Reviewed-on: https://chromium-review.googlesource.com/593559Reviewed-by: Jaroslav Sevcik <jarin@chromium.org>
Commit-Queue: Tobias Tebbi <tebbi@chromium.org>
Cr-Commit-Position: refs/heads/master@{#47001}