  The Chern-Simons axion coupling of a bulk insulator is only defined modulo a
quantum of e^2/h. The quantized part of the coupling is uniquely defined for a
bounded insulating sample, but it depends on the specific surface termination.
Working in a slab geometry and representing the valence bands in terms of
hybrid Wannier functions, we show how to determine that quantized part from the
excess Chern number of the hybrid Wannier sheets located near the surface of
the slab. The procedure is illustrated for a tight-binding model consisting of
coupled quantum anomalous Hall layers. By slowly modulating the model
parameters, it is possible to transfer one unit of Chern number from the bottom
to the top surface over the course of a cyclic evolution of the bulk
Hamiltonian. When the evolution of the surface Hamiltonian is also cyclic, the
Chern pumping is obstructed by chiral touchings between valence and conduction
surface bands.
