Can you be more specific about what you are looking for when it comes to chat? It sounds like you want an integration with your Project and a communication platform for general discussion on the project - correct me if I'm wrong here, however.
There are many chat integrations that work with GitLab right out of the box - with the most talked about being Slack as a lot of dev teams are using that anyway. With the Slack / GitLab integration you can have messages post to a certain channel based on certain events.
If you're looking for something a bit deeper, I would continue looking into Mattermost, which it seems like you have familiarity with already: https://about.gitlab.com/2015/08/18/gitlab-loves-mattermost/
Looking forward to hearing more about your project and your needs?