More about Oblivious HTTP and what Fastly is doing here is in a blog post that I wrote [1]. I wrote the OHTTP relay service for Fastly and was heavily involved in this deal.

Some points about how the service operates:

- Fastly does not receive your Chrome browsing history by virtue of running this service, because there is not a 1-1 mapping between URLs browsed and OHTTP requests made. We also cannot view the encapsulated request (which is passed to Google).

- Fastly does not capture access logs for this service, and no logs are sent to Google. There is only access to service-level metrics.

- Google does not have access to modify the configuration of this Fastly service, and does not own the domain or TLS key associated with it.

[1] https://www.fastly.com/blog/enabling-privacy-on-the-internet...