A $1064\mathrm{nm}$ pumped continuous-wave, mid-IR ( $3–4\mathrm{\mu m}$ ), signal-wave resonant optical parametric oscillator is frequency stabilized at the kilohertz jitter level to the transmission peak of an external high-finesse Fabry–Perot cavity. Owing to the high stability of the resonator length against acoustical perturbation, fine pump tuning of the idler wave around $3.3\mathrm{\mu m}$ results in an unprecedented mode-hop-free continuous scan over $500\mathrm{GHz}$ ( $17{\mathrm{cm}}^{-1}$ ).