We report on what is to our knowledge the first continuous-wave (cw) optical parametric oscillator (OPO) that is pumped by a tunable fiber laser. The OPO is singly resonant for the signal wave and consists of a 40-mm-long periodically poled LiNbO3 crystal in a four-mirror ring cavity. At a pump power of 8.3 W provided by the wavelength-tunable Yb-doped fiber laser, the singly resonant OPO generates 1.9 W of 3200-nm cw idler radiation. The singly resonant OPO was tuned from 1515 to 1633 nm (signal) and from 3057 to 3574 nm (idler) by means of the crystal temperature and poling period. We obtained a wide idler tuning range, from 2980 to 3700 mn, by tuning the wavelength of the fiber laser from 1032 to 1095 nm.