In environmental health studies air pollution measurements from the closest monitor are commonly used as a proxy for personal exposure. This technique assumes that air pollution concentrations are spatially homogeneous in the neighborhoods associated with the monitors and consequently introduces measurement error into a resultant model. To model the relationship between maternal exposure to air pollution and birth weight, we build a hierarchical model that accounts for the associated measurement error. We allow four possible scenarios, with increasing flexibility, for capturing this uncertainty. In the two simplest cases, we specify models with a constant variance term and a variance component that allows uncertainty in the exposure measurements to increase as the distance between maternal residence and the location of the closest monitor increases. In the remaining two models, we introduce spatial dependence using random effects. The models are illustrated using Bayesian hierarchical modeling techniques that relate pregnancy outcomes from the North Carolina Detailed Birth Records to air pollution data from the U.S. Environmental Protection Agency.