The hydroperoxy radical (HO2) plays a critical role in Earth's atmospheric chemistry as a component of many important reactions. The self-reaction of hydroperoxy radicals in the gas phase is strongly affected by the presence of water vapor. In this work, we explore the potential energy surfaces of hydroperoxy radicals hydrogen bonded to one or two water molecules, and predict atmospheric concentrations and vibrational spectra of these complexes. We predict that when the HO2 concentration is on the order of 10(8) molecules(.)cm(-3) at 298 K, that the number of HO2 center dot center dot center dot H2O complexes is on the order of 107 molecules(.)cm(-3) and the number of HO2 center dot center dot center dot(H2O)(2) complexes is on the order of 10(6) molecules(.)cm(-3). Using the computed abundance of HO2 center dot center dot center dot H2O, we predict that, at 298 K, the bimolecular rate constant for HO2 center dot center dot center dot H2O + HO2 is about 10 times that for HO2 + HO2.