Line-of-sight-attenuation chemical species tomography is a diagnostic in which the spatial distribution of a gaseous species is reconstructed from line-of-sight light-absorption measurements. In this approach, the measurement field is discretized into pixels wherein the species concentration of interest is presumed constant. Because the number of pixels needed to resolve the spatial features of interest almost always exceeds the number of measurement paths, additional assumptions about the distribution must be incorporated into the analysis to identify a unique solution. This paper presents a Bayesian approach to tomographic reconstruction, which formalizes the distinct roles of measurement data and prior information in the construction of an a posteriori distribution estimate. This technique was tested on a large-eddy simulation of a turbulent free-shear methane jet. Three forms of prior information were tested, ordered from most-to-least informative: the spatial covariance data from the simulation; a squared-exponential approximation of the spatial covariance; and a first-order Tikhonov matrix, which operated as a basic spatial-smoothness prior. Preliminary results show reconstruction accuracy improves with increasingly informative priors.