Following the steps outlined in this guide you’ll be able to install the full fledged version of Spotify (not the web based or Android App) on your Chromebook!
The stars have aligned! Spotify supports Linux, Chromebooks can run Linux – and now the final piece – audio works in Linux apps installed on Chromebooks. So without further ado, here’s how you can install Spotify for Linux on your Chromebook.
curl -sS https://download.spotify.com/debian/pubkey_0D811D58.gpg | sudo apt-key add –
echo “deb http://repository.spotify.com stable non-free” | sudo tee /etc/apt/sources.list.d/spotify.list
sudo apt-get update && sudo apt-get install spotify-client