I know this probably isn’t the most useful, but I did go ahead and run through the ‘happy path’ on CLI and everything looks great 
Requesting path without logging in (no cookie)
Logging in then requesting /chat, getting 200 with page content
So I guess I’d just recommend trying it again after dumping your browser cache? When you logout with Netlify Identity (click the logout button) it should clear everything, but I’m not sure why your particular local browser isn’t working for the moonface.ga site.

