  Motivated by cold atom experiments on Chern insulators, we study the
honeycomb lattice Haldane-Hubbard Mott insulator of spin-$1/2$ fermions using
exact diagonalization and density matrix renormalization group methods. We show
that this model exhibits various chiral magnetic orders including a wide regime
of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates
and ultimately melts this tetrahedral spin crystal. From analyzing low energy
spectra, many-body Chern numbers, entanglement spectra, and modular matrices,
we identify the molten state as a chiral spin liquid (CSL) with gapped semion
excitations. We formulate and study the Chern-Simons-Higgs field theory of the
exotic CSL-to-tetrahedral spin crystallization transition.
