Apparently some of the more popular feed readers can’t handle HTTP authentication, SSL feeds, or a combination of the two. No matter! GitHub private feeds are now accessible via a private token.
Note that whenever you change your password, your token will change. This is a feature - if you’re ever worried about your token getting out there, just change your password.
The old, HTTP authenticated feeds still work without a token, too.
Update: Thanks to Mislav, the feed now validates (whoops) and works over SSL.