We propose a theoretical framework for analyzing three-body hadronic B meson decays based on the perturbative QCD approach. The crucial nonperturbative input is a two-hadron distribution amplitude for final states, whose timelike form factor and rescattering phase are fit to relevant experimental data. Together with the short-distance strong phase from the b-quark decay kernel, we are able to make predictions for direct CP asymmetries in, for example, the B±→π+π−π± and π+π−K± modes, which are consistent with the LHCb data in various localized regions of phase space. Applications of our formalism to other three-body hadronic and radiative B meson decays are mentioned.