In this Rapid Communication, we address the chiral properties of valley exciton-polaritons in a monolayer of WS2 in the regime of strong light-matter coupling with a Tamm-plasmon resonance. We observe that the effect of valley polarization, which manifests in the circular polarization of the emitted photoluminescence as the sample is driven by a circularly polarized laser, is strongly enhanced in comparison to bare WS2 monolayers and can even be observed under strongly nonresonant excitation at ambient conditions. In order to explain this effect in more detail, we study the relaxation and decay dynamics of exciton-polaritons in our device, elaborate the role of the dark state, and present a microscopic model to explain the wave-vector-dependent valley depolarization by the linear polarization splitting inherent to the microcavity. We believe that our findings are crucial for designing novel polariton-valleytronic devices which can be operated at room temperature.