We present a universal upper bound on entropy. It is covariant and applies to surfaces of any shape, open or closed, at any place and time in all physical space-times. In particular, it remains valid in the interior of black holes and in all FRW cosmologies. It reduces to Bekenstein's bound whenever the latter is expected to hold. The new bound leads us to a generalised formulation of 't Hooft's
holographic hypothesis. We present an explicit construction for obtaining holographic screens in arbitrary space-times. Thus our formulation aims to establish the holographic principle not as a property only of static systems and of certain space-times, but as a truly universal law.