Why don't you connect that each Chat conversation start  in the same screen in Zoho Desk.?

So, here is the flow.

1. Chat is initiated 

2.Zoho Desk Ticket is created - and conversation is withing "ticket"
3. Once chat window is closed - ticket is "solved"

You don't have to call them tickets, but they could be all in the same window, and our agents should be in one tab handling Chat, Social, Tickets and phone calls...