We investigate the onset of convection for chemical-wave propagation in the Belousov-Zhabotinsky reaction based on the two-variable Oregonator model coupled with the fluid dynamic equations. For chemical waves in a vertical slab, two-dimensional convection occurs only for slab widths greater than a critical threshold width. The convective threshold is different for ascending and descending waves. Convectionless waves are flat and propagate with constant speed. Above the onset of convection, the wave velocity increases and the flat wave deforms due to two counterrotating steady rolls. For a horizontal slab, convection is always present and the wave velocity increases with increasing slab width. Our results are compared with experiments.