To enable ghost chat simply click the little red cross. That is click the close button instead of using the chat toggle key. From there on, the chat will only appear when someone talks, and will disappear again after a few seconds. In addition the chat appears somewhat transparent. It reduces clutter and adds a little to immersion. You can configure how long the ghost-chat should last in Options > GUI and Windows, along with the transparency level.

The default message mode is showed in the chat window input area. Left click it to cycle between 'GLOBAL', 'NEARBY' and 'GROUP'.