StartCom offers free SSL certificates that are recognized by most browsers: http://cert.startcom.org/
Heroku will still probably charge you a basic fee for enabling SSL, since each certificate requires a dedicated (non-shared) IP address... at least until SNI support becomes more commonplace.
Edit: Just to reiterate what others have said, this is a server-side certificate, which is primarily used for encryption. You'll also want to generate a client-side certificate for authentication purposes. That's something you'd do entirely on your own, no need to go through a third-party CA for that.
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StartCom offers free SSL certificates that are recognized by most browsers: http://cert.startcom.org/
Heroku will still probably charge you a basic fee for enabling SSL, since each certificate requires a dedicated (non-shared) IP address... at least until SNI support becomes more commonplace.
Edit: Just to reiterate what others have said, this is a server-side certificate, which is primarily used for encryption. You'll also want to generate a client-side certificate for authentication purposes. That's something you'd do entirely on your own, no need to go through a third-party CA for that.