I am trying to implement a realtime chat application using PHP . Is it possible to do it without using a persistent data storage like database or file . Basically what I need is
You didn't say it had to all be written it PHP :)
Install RabbitMQ, and then use this chat implementation built on top of websockets and RabbitMQ.
Your PHP is pretty much just 'chat room chrome'. It's possible most of your site would fit within the 5 meg limit of offline HTML5 content, and you have a very flexible (and likely more robust than if you did it yourself) chat system.
It even has 20 messages of chat history if you leave the room.
https://github.com/videlalvaro/rabbitmq-chat