In the context of supporting chemosynthesis and the potential for life, the most relevant compound among the options listed would be **methane**.
Methane can be produced by microorganisms through various metabolic processes, including methanogenesis, which is a form of anaerobic respiration. The presence of methane, along with other compounds like hydrogen sulfide or carbon dioxide, would indicate potential biological activity and support the idea of chemosynthesis.
While oxygen is important for aerobic life, its presence alone does not necessarily indicate life, as it could also be produced through abiotic processes. Hydrogen peroxide and glucose are less directly related to chemosynthesis in the context of life-supporting processes.
Therefore, the most appropriate choice regarding chemosynthesis indicating life support would be **methane**.