The response of a two-layer quasigeostrophic ocean model to basin scale stochastic wind forcing is investigated. As found in many previous studies, long Rossby waves are excited at the eastern boundary of the square model basin and the waves are baroclinically unstable. A novel aspect we focus on here is that the instability leads to the generation of zonal jets throughout the domain. The jets are actually wave-like in nature, and result directly from the instability. The “jets” appear when averaging the oceanic zonal velocity field over fixed periods of time. The longer the averaging period, the weaker the jets as the latter are in fact time-varying. The jets occur for a wide range of stratification, strength of stochastic forcing and the presence or not of a time mean circulation. The mechanism of jet generation described here thereby provides an explanation for the recent observations of alternating zonal jets in the mid-latitude oceans.