If you want build an easy chat site, user to user. You can use server send javascript event. Your chat site will be completed in a few hours.
Here is my demo: Server send event demo javascript in Laravel framework
Link github: https://github.com/tungkhac/Laravel-Demos/tree/chat_with_server_sent_event
Start testing:
Step 1:
Import database in db_backup folder in root
Step 2:
Create a virtual domain (optional)
Step 3:
Access follow Url: your_domain/chat. Per browser as a user, because I using cookie to determined user.
This is test and you can customize follow your idea.
Goodluck!