It is possible to set your status to appear invisible when using Gmail, iGoogle or orkut chat. While signed in as Invisible, you'll appear offline to your contacts. However, you can still start a chat with any of your online contacts while you are in this status.
To go invisible, select Invisible from the status drop-down menu in your chat list.
If you don't want a particular user to be able to see your online status, you can block that user. Once blocked, though, you won't be able to see their status, and you won't be able to communicate with them through chat.
Note: If you are signed in to chat with a status of invisible in one location like Gmail, but signed in a second time with an active status using another client, you will appear online to your contacts. Additionally, the Google Talk client does not support invisible status.