Using linear perturbation theory, the effect of a slightly viscous gas on the stability of a viscous jet is estimated. The gas flows in the direction of the jet axis. The perturbation in the gas is supposed to be governed by the equations for an inviscid, incompressible fluid, but the gas viscosity is taken into account to a first approximation by means of an energy balance. The method is shown to give correct answers for a viscous jet in a vacuum. For the case of uniform gas velocity the results agree with those of earlier work by Weber and by Levich. In this case the effect of the gas viscosity is very small. For nonuniform gas flow, using a logarithmic velocity profile, solutions are found for the two limiting cases in which the gas velocity is either large or small compared with the wave velocity. The results for these two limiting cases do not differ greatly from each other and predict that the gas flow has a substantial stabilizing effect on the jet when the gas velocity is large.