Weighting methods are used in observational studies to adjust for covariate imbalances between treatment and control groups. Entropy balancing (EB) is an alternative to inverse probability weighting with an estimated propensity score. The EB weights are constructed to satisfy balance constraints and optimized towards stability. Large sample properties of EB estimators of the average causal treatment effect, based on the Kullback-Leibler and quadratic Rényi relative entropies, are described. Additionally, estimators of their asymptotic variances are proposed. Even though the objective of EB is to reduce model dependence, the estimators are generally not consistent unless implicit parametric assumptions for the propensity score or conditional outcomes are met. The finite sample properties of the estimators are investigated through a simulation study. The average causal effect of smoking on blood lead levels is estimated using data from the National Health and Nutrition Examination Survey.