Unfortunately, I'm having trouble integrating the Markitup code into a Chrome App primarily because of the Content Security Policy : http://developer.chrome.com/extensions/contentSecurityPolicy.html. The Markitup code uses eval function and "Cross-Origin XMLHttpRequest".
The rendering part is really easy thanks to Asciidoctor.js so I was thinking, why not using http://ace.c9.io/ as editor and just add a preview frame ?
There is already a Chrome Extension that integrates Ace editor to create a text editor, so I guess this will be pretty easy : https://github.com/tylerlong/slim_text