You can use the bookmarklet when you are browsing GitHub and open a Jupyter Notebook. Just click the bookmarklet and it will open the notebook in Colaboraty where you can run it.
News: The Colab team released an extension that does the same.
To install it, drag this to your bookmark bar: Colaboratory for GitHub
If this does not work, you can:
@domoritz made this page based off of this tweet.