A 5 mm thick and 38 mm long 5% MgO-doped periodically poled lithium niobate (MgO:PPLN) cylinder with a grating period of 28 μm has been engineered as a partial cylinder with an angular aperture of 45°. An optical parametric oscillator based on this crystal and pumped at 1.064 μm is reported. The output energy is comparable to that generated in the same kind of sample cut as a slab, but the wavelength tunability from 1.41 to 4.3 μm is much broader and continuous.