The diversity of extrasolar planets discovered in the last decade shows that we should not be constrained to look for life in environments similar to early or present-day Earth. Super-Earth exoplanets are being discovered with increasing frequency, and some will be able to retain a stable, hydrogen-dominated atmosphere. We explore the possibilities for photosynthesis on a rocky planet with a thin H2-dominated atmosphere. If a rocky, H2-dominated planet harbors life, then that life is likely to convert atmospheric carbon into methane. Outgassing may also build an atmosphere in which methane is the principal carbon species. We describe the possible chemical routes for photosynthesis starting from methane and show that less energy and lower energy photons could drive CH4-based photosynthesis as compared with CO2-based photosynthesis. We find that a by-product biosignature gas is likely to be H2, which is not distinct from the hydrogen already present in the environment. Ammonia is a potential biosignature gas of hydrogenic photosynthesis that is unlikely to be generated abiologically. We suggest that the evolution of methane-based photosynthesis is at least as likely as the evolution of anoxygenic photosynthesis on Earth and may support the evolution of complex life.