We propose and evaluate a Bayesian beta regression model for U.S. county poverty rates. Such a rate model could be an improvement to the U.S. Census Bureau's current small-area poverty approach of linearly modeling the logarithm of poverty levels. For small areas, some of which may have estimates of no poverty or all poverty, a zero-one inflated rate model can usefully account for estimated rates of 0 or 1. Using Bayesian computation techniques, we estimate the parameters of a zero-one inflated beta regression model. We compare the results to the Census Bureau's current small-area model for county poverty estimation.