We present the theoretical basis for an algorithm that retrieves vertical profiles of ozone concentration using measurements of light scattered from the limb of the atmosphere. Simulated radiances at wavelengths between 300 and 675 nm are inverted using the optimal estimation technique, producing a retrieved ozone number density profile between 10 and 55 km. A detailed sensitivity analysis of this ozone retrieval algorithm follows. The largest source of ozone retrieval error is tangent height misregistration (i.e., instrument pointing error), which is relevant throughout the altitude range of interest and produces retrieval errors on the order of 10--20% due to a tangent height registration error of 0.5 km. The retrieved profile is shifted in altitude relative to the true profile, with very little distortion of the profile shape. Sensitivity to stratospheric aerosol is also a significant source of error, with errors of 5--8% for altitudes less than 40 km under background aerosol conditions when an aerosol-free atmosphere is assumed by the algorithm. Using an incorrect a priori ozone estimate can produce errors up to 15% at altitudes near 10 km, but the a priori profile has little influence above that level. Addressing these error sources (e.g., with better instrument pointing knowledge, introduction of reliable aerosol information, and better instrument signal-to-noise to reduce the importance of the a priori ozone estimate, respectively) is the key to significantly improving the retrieval accuracy. Further improvement would then be limited by several secondary error sources that produce retrieval errors at the 5% level.