The frequency stability of a cw optical parametric oscillator (cw OPO) near the signal-idler degeneracy has been studied. The strong tendency of a near-degenerate OPO to mode hop has been suppressed by using a bulk Bragg grating as a spectral filter in the OPO cavity. An experimental demonstration of stable parametric oscillation in a single longitudinal mode of the OPO cavity is reported, together with the capability of tuning the signal-idler difference frequency from 1 to 4 THz. The OPO has potential use in cw terahertz generation.