This paper gives the first demonstration of high-power, continuously tunable, narrowband radiation that is produced by means of a free-electron laser (FEL) in the far-infrared region of the electromagnetic spectrum. A Fox-Smith intracavity étalon was used to induce phase coherence between the 40 optical micropulses that were circulating in the laser cavity. The corresponding phase-locked spectrum consisted of a comb of discrete frequencies separated by 1 GHz. A pair of external Fabry-Pérot étalons was used to filter out a single line from this spectrum. The power in the selected narrow line at 69 microm wavelength was equal to 250 mW during the macropulse of the laser. The spectral width of the selected line is as small as that of a single cavity mode, i.e., a fraction of 25 MHz, in single macropulses of the laser. The average bandwidth of 25 MHz is determined by mode hopping of the phase-locked FEL. The selected frequency hops over 25 MHz between the extrema of this band. The influence of partially coherent spontaneous emission and mode hopping on the final linewidth was studied. The narrow-linewidth radiation was scanned in frequency over 1 GHz. We show that the possibilities to scan over smaller or larger frequency intervals are unlimited.