The accuracy of the Markov chain Monte Carlo procedure, Gibbs sampling, was considered for estimation of item and ability parameters of the one-parameter logistic model. Four data sets were analyzed to evaluate the Gibbs sampling procedure. Data sets were also analyzed using methods of conditional maximum likelihood, marginal maximum likelihood, and joint maximum likelihood. Two different ability estimation methods, maximum likelihood and expected a posteriori, were employed under the marginal maximum likelihood estimation of item parameters. Item parameter estimates from Gibbs sampling were similar to those obtained from the expected a posteriori method. (Contains 12 figures, 23 tables, and 60 references.) (Author)