No. Even if you have a PGP key on your Keybase profile, these messages are only encrypted with your Keybase device + paper keys. People aren't so great at managing and moving PGP private keys around, so PGP keys are not included in our chat or filesystem. You can read more about our key model here. The basic idea here is that non-technical people won't get confused and do something irresponsible.
Key additions must be signed publicly into your signature chain by a currently active key, as determined by your signature chain. This is verified by everyone you chat with. You'll see this policy in action when you install Keybase on a 2nd computer. It'll make you either (a) type something on your first computer, or (b) enter a paper key. This isn't just two-factor auth with server trust. The old key is signing a statement about the new key, and the new key is countersigning. If someone were to steal a device of yours that wasn't revoked, they could use it to read your data (of course), and therefore provision another new device. But that would be publicly discoverable because of the new device name announced in your signature chain. If you lose all of your devices and paper keys, you will lose your data. Keybase cannot read any of your encrypted data. So it's extra important to make sure you have at least 2 devices or paper keys. Maybe even 3, if you start caring about your data in Keybase. When our mobile apps launch, your phone will be a great device for provisioning and chatting.
This version supports muting individual conversations, so you're not interrupted and can ignore conversations that you're not interested in. More advanced blocking / reporting / nuking features will be available in an upcoming release.
Like with most chat apps, the Keybase servers will see who you're looking up. For a given message, Keybase servers know who sent it, approximate size, who the recipients are, and an ID for the channel. All of this is a requirement for performance and (upcoming) mobile notifications. It's better than PGP because of many modern crypto best practices, easier and safer key management, and easier and safer identity lookups. If your biggest fear is hiding whom you're talking to, none of the apps mentioned on this page are safe unless you're coming in over Tor, with no info connected to your real identity, in a library or cafe, and wearing a disguise.
Play with it, please, and let us know what features you want added.