TL;DR - Of course, you can use Clojurescript to develop Chrome Extensions. So, that's not the topic of this post. I've only documented how you'd set up your project, using the latest versions (as of this post's publishing) of piggieback and weasel.
Why Weasel? Because, as its author explains
A WebSocket transport is simple and avoids some of the thornier bugs caused by the CrossPageChannel transport, which is used in the standard ClojureScript browser REPL and Austin.