Major league baseball in the United States is divided into two leagues and four divisions. Each team plays 162 games against teams in the same league. The winner in each division is the team winning the most games of the teams in that division. We wish to predict the division winners based on games played up to any specified time. We use a generalized choice model for the probability of a team winning a particular game that allows for different strengths for each team, different home advantages, and strengths varying randomly with time. Future strengths and the outcomes of future games are simulated using Markov chain sampling. The probability of a particular team winning the division is then estimated by counting the proportion of simulated seasons in which it wins the most games. The method is applied to the 1991 National League season.