Fluorescence antibunching from single terrylene molecules embedded in a cholesteric-liquid-crystal host is used to demonstrate operation of a room-temperature single-photon source. One-dimensional (1-D) photonic-band-gap microcavities in planar-aligned cholesteric liquid crystals with band gaps from visible to near-infrared spectral regions are fabricated. Liquid-crystal hosts (including liquid crystal oligomers and polymers) increase the source efficiency, firstly, by aligning the dye molecules along the direction preferable for maximum excitation efficiency (deterministic molecular alignment provides deterministically polarized output photons), secondly, by tuning the 1-D photonic-band-gap microcavity to the dye fluorescence band and thirdly, by protecting the dye molecules from quenchers, such as oxygen. In our present experiments, using oxygen-depleted liquid-crystal hosts, dye bleaching is avoided for periods exceeding one hour of continuous 532 nm excitation.