We present Maximum Entropy (MaxEnt) reconstructions of krill distribution and estimates of mean krill density within two survey boxes of dimensions 80 km x 100 km to the north east and north west of South Georgia. The reconstructions are generated from acoustic line transect survey data gathered in the boxes in austral summers 1996 – 2000. Krill densities had previously been determined at approximately 0.5 km intervals along transect for each of the ten 80 km transects in each box, providing about 1600 krill density estimates per box. The MaxEnt technique uses a Bayesian approach to infer the most probable krill density for each of the 32000 0.5 km x 0.5 km cells in each survey box, taking explicit account of the spatial relationship between densities in the observed data. Despite some very large interannual and regional (east box cf west box) differences in mean krill density, the MaxEnt approach seems to work well, providing plausible maps of distribution. The technique also yields mean krill densities for which the confidence limits are often narrower than for estimates based upon more conventional (Jolly and Hampton, 1990) analyses.