We present a maximum entropy (MaxEnt) method for inferring stock density and mapping distribution from acoustic line-transect data. MaxEnt is founded on the bedrock of probability theory and allows the most efficient possible use of known data in the inference process. The method takes explicit account of spatial correlation in the observed data and seeks to reconstruct a distribution of density across the whole survey area that is both consistent with the observed data and for which the entropy is maximized. The method is iterative and uses the Bayesian approach of evaluating the posterior probability of a candidate solution under the constraint of the observed data to progress towards a converged solution. We apply the method to reconstruct maps of distribution of Antarctic krill throughout areas 100 x 80 km. Survey data were integrated at 0.5 km intervals along ten 80 km transects, giving approximately 1600 observed data. We inferred krill density for all 32000 0.5 x 0.5 km cells in the area. The method is computationally demanding but appears to work well, even in cases when the distribution of density is highly skewed. The MaxEnt technique has proved powerful for reconstruction of quantitative images from incomplete and noisy physical data (e.g. radio telescope data) and we suggest that it could be of benefit to the fisheries acoustic community, increasing the accuracy of acoustic estimates of stock density and generating superior maps of stock distribution.