During some phases of a neutron star's evolution, the temperature gradient in the surface layers, calculated assuming only radiative and conductive transport, may exceed the adiabatic gradient. This superadiabatic gradient is the necessary (but not sufficient) condition for convective instability. The present paper examines the sufficiency condition for the onset of convection in neutron stars in the presence of a strong magnetic field. It is shown that the large fields typically found in neutron stars--about 1011 to 1013 G--stabilize the atmosphere against convection. Convective instability can arise only in neutron stars with very weak magnetic fields, <=108-109 G. Convective motions in such weakly magnetized stars may be very rapid, with velocities as high as 1-10 km s-1. These energetic motions are likely to cause appreciable chromospheric and coronal heating.