We present a widely-tunable, singly-resonant optical parametric oscillator, emitting more than 1 W between 2.7 and 4.2 μm, which is phase locked to a self-referenced frequency comb. Both pump and signal frequencies are directly phase-locked to the frequency comb of a NIR-emitting fs mode-locked fibre laser, linked, in turn, to the caesium primary standard. We estimate for the idler frequency a fractional Allan deviation of ∼ 3 × 10⁻¹²τ⁻½ between 1 and 200 s. To test the spectroscopic performance of the OPO, we carried out saturation spectroscopy of several transitions belonging to the ν1 rovibrational band of CH₃I, resolving their electronic quadrupole hyperfine structure, estimating a linewidth better than 200 kHz FWHM for the idler, and determining the absolute frequency of the hyperfine components with a 50-kHz-uncertainty.