We demonstrate an eye-safe KTP-based optical parametric oscillator (OPO) driven intracavity by a diode-pumped 1064-nm Nd:YAG laser, passively Q-switched by a Cr4+:YAG crystal. The characteristics of this system, which operates at 1570 nm with a repetition rate as high as 50 Hz, are studied as a function of Cr4+:YAG optical density. Under optimum conditions the OPO generates 1.5-mJ, 3.4 +/- 0.1-ns pulses in a single transverse mode. For a Cr4+:YAG Q-switch element with an optical density of 0.5 the conversion efficiency of the intracavity energy is approximately 45% with the ratio of OPO to Nd:YAG peak-pulse intensity exceeding unity. These and other OPO characteristics compare favorably with a simple rate equation model of the OPO dynamics.