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The effects of hydrogen on the growth kinetics of Si(0 0 1) during gas-source molecular-beam epitaxy from disilane are investigated with kinetic Monte Carlo simulations. The growth model includes the surface decomposition of disilane, which requires four mobile and reactive surface species: Si, H, SiH2and SiH3. Based on recent reflectance anisotropy measurements, the desorption of hydrogen is presumed to occur preferentially from step edges. Below approximately 400°C (where the model allows surface reactions to occur) the accumulation of surface hydrogen is found to prevent growth, but for temperatures above 600°C, where the surface lifetime of the hydrogen is relatively short, we find no significant differences in the overall growth features in comparison with a solid-source (no hydrogen) growth model of Si(0 0 1). At intermediate temperatures, where surface hydrogen atoms are present but do not prevent growth, we find a higher density of smaller islands and rougher propagating step edges in comparison with those of the solid-source model. Anisotropic morphological features, which are characteristic signatures in the solid-source model, are suppressed by the surface hydrogen atoms in the gas-source model.