The collision of He2+ with H(1s) is studied in the impact parameter (eikonal) approximation by expanding the wavefunction on a set of electronic states of the molecule HeH2+. Exact eigenenergies and matrix elements between the states of this basis set are used in the calculations. The results for the total charge-exchange cross section are in good agreement with the experimental data. The structures observed experimentally in the variation of the charge-exchange probability as a function of energy for a fixed scattering angle are fairly well reproduced in the theory. However, the origin of these structures is not that proposed by Keever and Everhart (1966) on the basis of their experimental work.