You will not need a fresh and separate copy of Icon.
You will not even need a fresh and separate copy of Tequila
Leo has had to delay the rollout of Paragon Chat, so it is not going in today. In order to get it, you will need to keep cold-booting Tequila from your desktop icon (small i) so that you get the updated version which will have Paragon Chat in it. When you do that, you will see a Tequila login screen that will look something like this
To get to Paragon Chat, you select Paragon Chat. This will pop up the smaller window that will ask for the Titan User Name and Password. Note that this is XMPP protocol, so if you have spaces in your name you will have to use _ instead. For instance, I would enter Victoria_Victrix.
Once you have done that, you select "Enter City of Heroes" which will take you to the Titan Chat Server.
[[EDIT: Emphasized that it's not available today, dag nabbit. ~Agge]]