More than 60 years ago, Dicke published a seminal paper on coherence in spontaneous radiation process by a collection of atoms. Superradiance has since attracted a lot of interest, from its first experimental observation in a fully inverted system in the 1970s to single photon superradiance in the 2000s. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to non radiative decoherence processes. They are thus much harder to populate and to observe. Avoiding decoherence effects by using a dilute cloud of laser-cooled atoms containing a large number of atoms, we report on direct observation of subradiance. In our experiment, we use a far detuned laser to avoid multiple scattering and detect the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we observe a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical thickness of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model.