  Hexagonally patterned two-dimensional $p$-type semiconductor systems are
quantum simulators of graphene with strong and highly tunable spin-orbit
interactions. We show that application of purely in-plane magnetic fields, in
combination with the crystallographic anisotropy present in low-symmetry
semiconductor interfaces, allows Chern insulating phases to emerge from an
originally topologically insulating state after a quantum phase transition.
These phases are characterized by pairs of co-propagating edge modes and Hall
conductivities $\sigma_{xy} = +\frac{2 e^2}{h}, -\frac{2 e^2}{h}$ in the
absence of Landau levels or cyclotron motion. With current lithographic
technology, the Chern insulating transitions are predicted to occur in GaAs
heterostructures at magnetic fields of $\sim 5\text{T}$.
