A probabilistic Bayesian Maximum Entropy (MaxEnt) technique was used to estimate the abundance of Antarctic krill (Euphausia superba) across the Scotia Sea using data from the CCAMLR 2000 Krill Synoptic Survey of Area 48 (CCAMLR-2000 Survey) and to map the density distribution of krill across the survey area. Density values for the unsurveyed off-transect portions of the survey area were inferred, and thus values for total biomass across the survey area, and within individual small-scale management units (SSMUs), were estimated. Abundance in some of the individual SSMUs had not previously been estimated due to the sparseness of data in these regions. The MaxEnt formalism allows an objective choice of the parameters of the estimation method, and hence an objective choice of the most probable reconstruction of krill distribution, given the data. The Bayesian framework also allows intrinsic calculation of the error in the density estimates. The total biomass inferred for the survey area was 208 million tonnes, with a standard deviation of 10 million tonnes. The MaxEnt method provides new insights into the extremely sparse survey data (only 0.6% of the survey area was directly acoustically sampled), and enhances the conservation and management potential of the CCAMLR-2000 Survey.