1,523 votesTom commented
I'm not sure if it makes sense for protonmail to implement this, given there are many other services targeting encrypted chat.
However, if you do want to implement a chat service, please consider using http://matrix.org/ rather than signal. Signal is great, but does not have federation. So it acts as a walled garden.
If you implement matrix, you can host your own chat servers but also then let users chat to users on other servers.
Matrix also has bridges, which allow you to connect other chat services e.g. IRC.
If you would like to see how matrix works, have a look at https://riot.im/ which implements the matrix protocol.