Semiconductor microcavities offer unique systems in which to investigate the physics of weakly interacting bosons. Their elementary excitations, polaritons-mixtures of excitons and photons-can accumulate in macroscopically degenerate states to form various types of condensate in a wide range of experimental configurations, under either incoherent or coherent excitation. Condensates of polaritons have been put forward as candidates for superfluidity, and the formation of vortices as well as elementary excitations with linear dispersion are actively sought as evidence to support this. Here, using a coherent excitation triggered by a short optical pulse, we have created and set in motion a macroscopically degenerate state of polaritons that can be made to collide with a variety of defects present in the microcavity. Our experiments show striking manifestations of a coherent light-matter packet, travelling at high speed (of the order of one per cent of the speed of light) and displaying collective dynamics consistent with superfluidity, although one of a highly unusual character as it involves an out-of-equilibrium dissipative system. Our main results are the observation of a linear polariton dispersion accompanied by diffusionless motion; flow without resistance when crossing an obstacle; suppression of Rayleigh scattering; and splitting into two fluids when the size of the obstacle is comparable to the size of the wave packet. This work opens the way to the investigation of new phenomenology of out-of-equilibrium condensates.