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This CL replaces a var counter for fetching cookie data with javascript
promises. The counter had issues with reentrancy, while promise arrays
are more robust.

BUG=None
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:closure_compilation

Review-Url: https://codereview.chromium.org/2439233002
Cr-Commit-Position: refs/heads/master@{#427130}