The convective instability of a viscous liquid jet emanating into a inviscid gas with a swirl is investigated. Contrary to the known case of a swirling liquid jet in a quiescent gas, the swirl in the ambient gas is shown to have a stabilizing effect. The inertia force in the gas is shown to play dual roles of both stabilization and destabilization. The gas inertia associated with the swirl has a stabilizing influence, but that associated with the interfacial pressure fluctuation has a destabilizing effect. A physical explanation of the mechanism of stabilization by the gas swirl is given.