We present a gigahertz (GHz)-repetition-rate optical parametric oscillator (OPO) pumped by an electro-optic comb at 1.03 µm, delivering sub-picosecond signal pulses across 1.5-1.7 µm from a MgO-doped periodically poled LiNbO3 crystal. Using a pump power of 5 W at 14.2 GHz repetition rate, 378 mW of signal power is obtained at 1.52 µm from a subharmonic cavity, corresponding to a signal extraction efficiency of 7.6%. By cascading a Mach-Zehnder modulator, the pump pulse repetition rate can be divided by any integer number from one to 14, allowing the OPO to operate with a flexible repetition rate from 1 to 14.2 GHz. A strategy leading to quasi-continuous repetition rate tunability of the OPO is also discussed.