Hi @os_so 
Theme doesn’t matter, you need an app or chat service, shopify does not host executable code.
The theme systems is just that a THEME system, not a full blown web environment.
See a service like ably.com for message passing / real time communications.
Or just use discord etc.
Keep in mind to set realistic goals, if you don’t have a serious budget and your having to ask these types of questions in the first place your probably not gonna have a great time in managing the process and issues of a public chat room on top of trying to run an ecommerce business.