It is normal for maximum people who use facebook from a long time that sometimes s/he turn off chat in there to hide his/her activity from his/her other friends. It is also noted that facebook has recently added another feature by which you can hide your activity for some of your friends or show activity for some of your friends. But nowadays it is not as private as before.At before if you turned off your chat, your friends were unable to find you online from then. The were shown you as offline until you turn onat fac the chat in facebook. Suppose you turned off chat at 11:00 am and still browsing till 2:00 pm. In this case your friend will see you active 3 hours ago if s/he visit your profile at 2:00 pm and according to this. But now a days it is changed.
I have already said that you may not be turned off from chat if you do not use some specific version of facebook. It is also said here.
But today I have found more unsecured system of facebook. If you turn off your facebook chat and are browsing by a specific version of facebook but you may be shown online to your friends.
What is this? Yes, It is really. If yor friend use messenger app on android phone and come to your chat box s/he will see how long time ago you were at facebook. And it will show the exact time. So if you remain then online you will be shown as Online to your friend. So you will not be hide yourself from now.