Hey, i am an asp.net developer having 9 years of experience.
I have been working on webRTC kind of projects since very long. E.g. Whatsapp web clone, classmate a chat application, realtime notifications like Facebook web etc
Let me know if your web is in asp.net or not.
I have experience of making web based chat system.
I have also worked on sockets and Web RTC API. I assure you, you will get a quality product of web chat system in your website.