Understanding the impact that environmental exposure during different stages of pregnancy has on the risk of adverse birth outcomes is vital for protection of the fetus and for the development of mechanistic explanations of exposure-disease relationships. As a result, statistical models to estimate critical windows of susceptibility have been developed for several different reproductive outcomes and pollutants. However, these current methods fail to adequately address the primary objective of this line of research; how to statistically identify a critical window of susceptibility. In this article, we introduce critical window variable selection (CWVS), a hierarchical Bayesian framework that directly addresses this question while simultaneously providing improved estimation of the risk parameters. Through simulation, we show that CWVS outperforms existing competing techniques in the setting of highly temporally correlated exposures in terms of (i) correctly identifying critical windows and (ii) accurately estimating risk parameters. We apply all competing methods to a case/control analysis of pregnant women in North Carolina, 2005-2008, with respect to the development of very preterm birth and exposure to ambient ozone and particulate matter $<$ 2.5 $mu$m in aerodynamic diameter, and identify/estimate the critical windows of susceptibility. The newly developed method is implemented in the R package CWVS.