Electrons in image-potential states on the surface of bulk helium represent a unique model system of a two-dimensional electron gas. Here, we investigate their properties in the extreme case of reduced film thickness: a monolayer of helium physisorbed on a single-crystalline (111)-oriented Cu surface. For this purpose we have utilized a customized setup for time-resolved two-photon photoemission (2PPE) at very low temperatures under ultra-high vacuum conditions. We demonstrate that the highly polarizable metal substrate increases the binding energy of the first (n = 1) image-potential state by more than two orders of magnitude as compared to the surface of liquid helium. An electron in this state is still strongly decoupled from the metal surface due to the large negative electron affinity of helium and we find that even one monolayer of helium increases its lifetime by one order of magnitude compared to the bare Cu(111) surface.