Exact mathematical expressions are given for the bias and variance of the arithmetic and maximum likelihood estimators of the first moment (mean) of a lognormal distribution. On the basis of these exact expressions, and without the need for simulation, statistics on the bias and variance have been computed for a range of sample sizes and geometric standard deviations. The results reaffirm that an unbiased maximum likelihood estimator exists that has minimum variance. Contrary to some recent recommendations, this is the preferred estimator if the data truly come from a lognormal distribution.