Well, this is a bit vague.
Could you please tell us what you have already tried, what ideas you have, etc?
Doing so might be a lot more helpful and easier for us to point you to the right direction.
One of my suggestions, and as @idi527 said above, would be to search for articles, blog posts or maybe GitHub repositories which have chat applications written in Python or Ruby. As these programming languages are similar in syntax to Elixir, I believe it will be fairly easy to “translate” the code / flow of the application into Elixir or Phoenix.
This will also be a good way to evolve your Elixir skills and face a bit of a challenge.
Good luck mate!