This technical note studies the global output feedback stabilization problem for a chemostat with an arbitrary number of species competing for a single nutrient source. It is shown that coexistence can be achieved by means of a feedback control of the substrate input concentration and an appropriate choice of a constant dilution rate. The input substrate feedback controller proposed is a dynamic time-varying output feedback, with the substrate concentration considered as the output. The result relies on the construction of a novel nonlinear observer and is established via a Lyapunov-based proof.