  Topological insulator phases of non-interacting particles have been
generalized from periodic crystals to amorphous lattices, which raises the
question whether topologically ordered quantum many-body phases may similarly
exist in amorphous systems? Here we construct a soluble chiral amorphous
quantum spin liquid by extending the Kitaev honeycomb model to random lattices
with fixed coordination number three. The model retains its exact solubility
but the presence of plaquettes with an odd number of sides leads to a
spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram
displaying Abelian as well as a non-Abelian quantum spin liquid phases with a
remarkably simple ground state flux pattern. Furthermore, we show that the
system undergoes a finite-temperature phase transition to a conducting thermal
metal state and discuss possible experimental realisations.
