Chrome and Firefox can “talk” to each other via WebRTC: Process, Stakes and Opportunities.

It is already done; henceforth developers can offer rich, secure communications, integrated directly into their web applications. For those who unfamiliar, WebRTC is a set of technologies that brings clear voice, sharp high-definition (HD) video and low-delay communication to the web browser.
Therefore, for the first time, Chrome and Firefox can “talk” to each other via WebRTC. This means that Chrome and Firefox
can now communicate by using standard technologies such as the Opus and VP8 codecs for audio and video, DTLS-SRTP for encryption, and ICE for networking.

To see how it works, you’ll need desktop Chrome 25 Beta and Firefox Nightly for Desktop. In Firefox, you'll need to go to about:config and set the media.peerconnection.enabled pref to "true”. Then head over to the WebRTC demo site and start calling.

In regards to developers looking to include this functionality in their own apps, You can look at the source code of the AppRTC demo, a library that makes writing cross-browser WebRTC apps a snap, and a document detailing some of the minor differences between browsers.