We have investigated the time evolution of a jet of non-Brownian particles falling under the action of gravity in a viscous liquid at low Reynolds number. Different regimes have been observed depending on volume fraction and particle-to-jet diameter ratio. In particular, the jet has been found to be unstable and to develop varicose modulation of its diameter at low volume fractions. The dominant wavelength and saturated amplitude have been measured and are observed to decrease with increasing volume fraction. A simple numerical simulation using point particles is able to capture the major features of the instability.