The paper describes a Bayesian spatial discrete time survival model to estimate the effect of air pollution on the risk of preterm birth. The standard approach treats prematurity as a binary outcome and cannot effectively examine time varying exposures during pregnancy. Time varying exposures can arise either in short-term lagged exposures due to seasonality in air pollution or long-term cumulative exposures due to changes in length of exposure. Our model addresses this challenge by viewing gestational age as time-to-event data where each pregnancy becomes at risk at a prespecified time (e.g. the 28th week). The pregnancy is then followed until either a birth occurs before the 37th week (preterm), or it reaches the 37th week, and a full-term birth is expected. The model also includes a flexible spatially varying baseline hazard function to control for unmeasured spatial confounders and to borrow information across areal units. The approach proposed is applied to geocoded birth records in Mecklenburg County, North Carolina, for the period 2001-2005.We examine the risk of preterm birth that is associated with total cumulative and 4-week lagged exposure to ambient fine particulate matter.