A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z(2) topological insulators by time-reversal symmetry(1-3). Recently, interest has turned to unusual surface states in the large class of non-symmorphic materials(4-12). In particular, KHgSb is predicted to exhibit double quantum spin Hall states(10). Here we report measurements of the Hall conductivity in KHgSb in a strong magnetic field B. In the quantum limit, the Hall conductivity is observed to fall exponentially to zero, but the diagonal conductivity is finite. A large gap protects this unusual zero-Hall state. We theoretically propose that, in this quantum limit, the chemical potential drops into the bulk gap, intersecting equal numbers of right- and left-moving quantum spin Hall surface modes to produce the zero-Hall state. The zero-Hall state illustrates how topological protection in a non-symmorphic material with glide symmetry may lead to highly unusual transport phenomena.