The Orbiting Carbon Observatory (OCO) will measure the distribution of total column carbon dioxide in the Earth's atmosphere from an Earth-orbiting satellite. Three high-resolution grating spectrometers measure two CO2 bands centered at 1.61 and 2.06 mum and the oxygen A-band centered at 0.76 mum in the near infrared region of the spectrum. This paper presents the optical design and highlights the critical optical requirements flowed down from the scientific requirements. These requirements necessitate a focal ratio of f/1.9, a spectral resolution of 20,000, and precedence-setting requirements for polarization stability and the instrument line shape function. The solution encompasses three grating spectrometers that are patterned after a simple refractive spectrometer approach consisting of an entrance slit, a two-element collimator, a planar reflection grating, and a two-element camera lens. Each spectrometer shares a common field of view through a single all-reflective telescope. The light is then re-collimated and passed through a relay system, separating the three bands before re-imaging the scene onto each of the spectrometer entrance slits using an all-reflective inverse Newtonian re-imager.