Looks like the chat.stackexchange.com is trying to do some magic referrer sniffing to detect the site you're coming from. Alas, this doesn't work if you were using HTTPS, since browsers don't send referrer info when following an HTTP link from an HTTPS page.
Using a protocol-relative link to chat, so that chat would also be loaded over HTTPS, would be the optimal solution. Unfortunately, SE chat still breaks horribly over HTTPS, so that's not practical at the moment.
An alternative work-around is to inject the missing parameters back into the link on pages loaded over HTTPS, e.g. like this:
if ('https:' != location.protocol) return;
'href', 'http://chat.stackexchange.com/?tab=site&host=' +
Ps. While waiting for a proper fix, I have included this workaround in SOUP v1.12.