How to hide online status

Hi,

Unfortunately I do not have a Messenger System in front of me or I might be able to answer the question without hasseling this forum.

How can a user hide their online status? The problem is that the customer takes user privacy very seriously and before they even think about implementing Messenger they want to be sure that a user can hide their online status if they want to. Is this possible? If so, how?

Thank you for your assistance.

Mike