In this work we will present a method for retrieving nighttime electron density profiles from OI 135.6 nm limb emissions measured by the Global Ultraviolet Imager (GUVI) aboard the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) mission spacecraft. The primary mechanism for 135.6 nm radiance in the nighttime thermosphere is recombination of O+ ions, and the volume emission rate is approximately proportional to the square of the electron density. Herein we describe a two-step inversion method in which we first determine the volume emission rate as a function of altitude from the radiance measurements and then use the inferred volume emission rates to determine the electron density profile. There are two important factors that we have addressed in constructing the retrieval algorithms for this problem. First, the GUVI instrument was primarily designed for day side measurements. Consequently, the signal levels on the night side are very low, and our retrieval algorithms must therefore be able to function in regions where the signals are weak. Second, since we must take the square root of the volume emission rate, it must be everywhere positive in order for the electron density to be deduced. For this reason, we have imposed nonnegativity constraints (using the methods described by Menke <1989>) on what might otherwise be discrete linear retrievals of volume emission rate. After describing the retrieval method we present an error analysis and a preliminary comparison with coincident measurements by incoherent scatter radars (ISRs). In general, the retrieved electron densities from the GUVI data agree well with the ISR data, although more coincident measurements would increase our confidence in the resulting electron density profiles.