A novel double hydrogen atom exchange process, HX + H'O-2 -> H'X + HO2 for the halogen series X = F, Cl, Br, and I, is identified using theoretical methods. These concerted reactions are mediated through a stabilized five-membered planar ring transition state structure. The transition state barrier for the double exchange process is found to be significantly lower than that for the abstraction reaction of a single hydrogen atom. Density functional theory employing the M11 exchange functional is used to compute parameters of the potential energy surface and the rate coefficients are obtained using transition state theory with small curvature tunneling. For low temperatures, the exchange reaction proceeds at a rate several orders of magnitude faster than the abstraction channel, which is also calculated. The exchange process may be observed using isotope scrambling reactions; such reactions may contribute to observed isotope abundances in the atmosphere. The rate coefficients for the isotopically labeled reactions are computed. It is found that the trends in reactivity within the series of halogen reactions can be quantitatively understood using the degree of electron delocalization at the transition state. The barriers are found to fall as the electronegativity of the halogen atom decreases.