I wondered if there was a solution to play around with Drupal 8 on a Chromebook (super cheap hardware / "everything in the cloud model" with a 16G SSD).
After some reddit I discovered that Koding.com provides you freely, in the browser, a VM / terminal plus a text editor for PHP and other popular languages (Ruby, Python, ...).
Open up your Koding Terminal and cd in the Web directory (default, single docroot for a VM).
Git clone the latest dev (8.0.x) release in the current directory.
git clone --branch 8.0.x http://git.drupal.org/project/drupal.git .
Drupal requires the gd library to be insalled.
sudo apt-get update
sudo apt-get install php5-gd
If you haven't installed MySQL yet.
sudo apt-get install mysql-server mysql-common mysql-client
After setting the MySQL credentials, install the PHP extension
sudo apt-get install php5-mysql
Create the database
echo 'CREATE DATABASE drupal8' | mysql -u root -p
Restart Apache to apply changes (GD, MySQL)
sudo service apache2 restart
Return in the Drupal root directory if needed (~/Web in this example).
Make your own copy of the settings files, to be writed by the Drupal installer (single site install).
cp default.services.yml services.yml
cp default.settings.php settings.php
sudo chmod a+w services.yml settings.php
Create the files directory and make it writeable.
sudo chmod a+w -R files
Head now to your Koding domain (http://username.koding.io) to install Drupal.
Since July 2015, Digital Ocean also takes care of the hosting : http://blog.koding.com/2015/07/byo-vm/