The structure of the hydrogen-air counterflow diffusion flame is investigated by Damkohler number asymptotics. Attention is restricted to flowfield strain times smaller than dissociation times but larger than the characteristic chemical time of three-body recombination reactions, thereby placing the system on the upper, vigorously burning branch of the characteristic S-curve of peak temperature as a function of strain time without equilibrium broadening. Under these conditions, it is Shown that the reactants can coexist only within a thin reaction zone separating two radical-free equilibrium regions. First, the equations for the counterflow mixing layer in the two outer equilibrium regions are solved in the classical Burke-Schumann limit by the introduction of appropriate conserved scalars that account for variable transport coefficients and variable Schmidt numbers,different for different species. Then, the reaction zone is investigated with scaling that identifies the relevant reduced Damkohler number. While the solutions in the outer zones are peculiar to the counterflow configuration because of their convective-diffusive character, the reactive-diffusive nature of the reaction zone at leading order enables its structure in transformed coordinates to be expressed independently of the geometrical configuration. Matching the solutions from the inner reaction region with those from the outer equilibrium regions yields the first-order asymptotic solution to the problem, which compares favorably with results obtained by numerical integration of the full conservation equations with detailed chemistry and transport descriptions. In particular, the reason that the maximum radical concentration and temperature deficit vary linearly with the one-third power of the strain rate is explained.