We demonstrate a synchronously-pumped optical parametric oscillator (OPO) with a cavity formed from high refractive index inverted prisms, also known as Brewster mirrors. Exploiting a single total internal reflection, this is the simplest device capable of deviating a laser beam by 180∘. The OPO produced a chirped signal output tunable from 1060-1570nm with a maximum power of 114 mW. We investigate the geometric properties of ideal and imperfect Brewster mirror prisms and find the latter can provide ∼1000 × finer control of the signal wavelength when compared to cavity length tuning.