We report a portable, all-solid-state, mid-infrared spectrometer for trace-gas analysis. The light source is a continuous-wave optical parametric oscillator based on PPLN and pumped by a Nd:YAG laser at 1064 nm. The generated single-frequency idler output covers the wavelength region between 2.35 and 3.75 μm. With its narrow line width, this light source is suitable for precise trace-gas analysis with very high sensitivity. Using cavity leak-out spectroscopy we achieved a minimum detectable absorption coefficient of 1.2×10-9 /cm (integration time: 16 s), corresponding, for example, to a detection limit of 300 parts per trillion ethane. This sensitivity and the compact design make this trace-gas analyzer a promising tool for various in situ environmental and medical applications.