Can browsers connect to a proxy over SSL/TLS?

Question

If I set up a proxy (such as Squid for example) configured with certs to listen for HTTPS are browsers able to connect to the proxy over TLS/SSL?

Example of what I'm asking:

Browser Proxy Server yahoo.com -> TLS -> Squid -> HTTP -> yahoo.com

I've set up a proxy listening on 443, but am not having success getting browsers to use it (connecting to the http proxy on port 80 works fine).

Answer 1

Chrome can do that: http://www.chromium.org/developers/design-documents/secure-web-proxy

It also supports a directive in PAC file to point to HTTPS proxy.