If part of a population is hidden but two or more samples are available that each cover parts of this population, multiple systems estimation can be applied to estimate the size of this population. A problem is that these estimates suffer from finite-sample bias that can be substantial in case of a small sample or a small population size. This problem was recognized by Chapman, who derived his essentially unbiased Chapman-estimator for two samples. Because more than two samples may be required to correct for sample dependence, we propose a Generalized Chapman-estimator that can be applied with any number of samples. In a Monte Carlo experiment, this new estimator shows hardly any bias and has smaller standard errors than competing bias-reduced estimators. It is also compared to the usual maximum likelihood estimates for the case of estimating the number of homeless people in the Netherlands, where it shows notably different outcomes.