Real-time Web-based Chat System

I need a real-time chat system for my website, implemented using a web-based platform like WebSocket. The chat system should support both group chat and private messaging.

Requirements:
- Real-time communication
- WebSocket implementation
- Group chat functionality
- Private messaging capability

Ideal Skills and Experience:
- Proficiency in WebSocket and web development
- Experience in building real-time chat applications
- Strong knowledge in backend and frontend integration

Please provide examples of similar work done. Looking forward to your proposals!