Can I write Chrome extensions in Elixir?

Chrome Extensions  |  Chrome for Developers

There is no BEAM on browsers so that is out of the question. But given that JavaScript is involved it may be possible to use Elixirscript (i.e. no processes; elixirscript-book).

But taking on the burden of cross-compilation and JavaScript interop, I’d look into using Bucklescript or ReasonML to also get the benefit of static typing.