How do I add Chatter onto a visualforce page? Is it possible ?

Yes, these are Chatter Components for Visualforce. The simplest example to try out would be to create a page like this

<apex:page >
  <chatter:feed entityId="{!$User.Id}"/>
</apex:page>

This will display the Chatter feed for the currently logged in user. The entityID here can be the ID of a standard object, custom object, user etc.

You can read more each of these components here. Obviously, you can write your own Apex controllers and do a lot of custom Chatter functionality as well. One such example is listed here.