Using a continuous-wave Type II optical parametric oscillator below threshold, we have demonstrated a novel source of heralded single photons with high fidelity. The generated state is characterized by homodyne detection and exhibits a 79% fidelity with a single-photon Fock state (91% after correction of detection loss). The low admixture of vacuum and the well-defined spatiotemporal mode are critical requirements for their subsequent use in quantum information processing.