This reverts commit CL 103975 (a9b799a2).

Reason for revert: adds data race, breaks race builders, and Brad forgot
to run the Trybots.

Change-Id: Id227dad7069560dbb3ea978a1dcd77ce1979034e
Reviewed-on: https://go-review.googlesource.com/104015Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>