We present a narrow-linewidth, singly-resonant cw optical parametric oscillator, emitting more than 1 W in the 2.7–4.2 µm range. The OPO is pumped by a narrow linewidth (40 kHz) fibre-laser system and the signal frequency is locked to a high-finesse Fabry–Pérot cavity in order to increase the spectral resolution, thus obtaining a residual linewidth of 70 kHz for the signal. We tested the spectral performance of our OPO on several transitions in the ν1 rovibrational band of CH3I, measuring line intensities and showing sub-Doppler dip detection.