We study the effect of introducing hydrogen gas through the RF plasma source during plasma-assisted molecular beam epitaxy of GaN(0001). The well-known smooth-to-rough transition that occurs for this surface as a function of decreasing Ga flux in the absence of H is found to persist even with H present. But, the critical Ga flux for this transition is increased by the presence of H, and for sufficiently high H pressure a new 2 × 2 surface structure that is believed to be H-terminated is observed. Under Ga-rich conditions, the presence of hydrogen is found to induce step bunching on the surface, from which we argue that H selectively bonds to surface step and/or kink sites.