Update! cPanel supports LetsEncrypt, but you just need to install the plugin for it to work. To do this, run:

/scripts/install_lets_encrypt_autossl_provider

Once installed, Let’s Encrypt will appear in WHM’s Manage AutoSSL interface (Home >> SSL/TLS >> Manage AutoSSL) where you can enable the provider.

At the time of this writing, LetsEncrypt is in public beta and already in high demand. This service is a new certificate authority that allows you to generate your own signed certificates in an effort to improve security.  At present there is a feature request for providing this functionality in cPanel.

You can also use this handy (commercial) plugin: https://letsencrypt-for-cpanel.com/

Update: Sources for an open-source plugin have been released here:

https://github.com/Prajithp/letsencrypt-cpanel

I’m not going to go through the process of copying and pasting verbatim instructions, but you can find the entire write-up on the cPanel forums here:

https://forums.cpanel.net/threads/how-to-installing-ssl-from-lets-encrypt.513621/