The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian estimation, and marginal maximum likelihood estimation methods. Data were simulated with 100 or 300 examinees and 15 or 45 items. Two different priors, informative and uninformative, were employed in the MCMC procedure. Marginal Bayesian estimation yielded consistently smaller root mean square differences and mean Euclidean distances than the other estimation methods. An appendix provides additional information about the computations. (Contains 6 tables, 5 figures, and 52 references.) (SLD)