We introduce the ON-OFF privacy problem. At each time, the user is interested in the latest message of one of N online sources chosen at random, and his privacy status can be ON or OFF for each request. Only when privacy is ON the user wants to hide the source he is interested in. The problem is to design ON-OFF privacy schemes with maximum download rate that allow the user to obtain privately his requested messages. In many realistic scenarios, the user's requests are correlated since they depend on his personal attributes such as age, gender, political views, or geographical location. Hence, even when privacy is OFF, he cannot simply reveal his request since this will leak information about his requests when privacy was ON. We study the case when the users's requests can be modeled by a Markov chain and N=2 sources. In this case, we propose an ON-OFF privacy scheme and prove its optimality.