Zonal wind (ZW) generation by thermal convection in rotating spherical shells is studied using numerical calculations. Strong ZW accompany quasi-geostrophic, high Rayleigh number convection in shells with stress-free boundaries. In a thin shell (radius ratio 0.75) with stress-free boundaries, nearly 90% of the total kinetic energy is contained in the ZW at Rayleigh number 106 and Taylor number 4.4¿107. The same parameters in a thicker shell produce weaker convection and weaker ZW. Rigid boundaries reduce the kinetic energy in the ZW to less than 20% of the total. The ZW are eastward (prograde) in the equatorial region and westward at higher latitudes, and are driven by Reynolds stresses associated with the convection. Episodes with strong ZW alternate with episodes of strong convection. Although far from the dynamical regime of Jupiter and Saturn, our results support the interpretation that the prograde equatorial jets on these planets originate from deep convection. ¿ 2001 American Geophysical Union