  We study the Kitaev-Heisenberg-$\Gamma$-$\Gamma'$ model that describes the
magnetism in strong spin-orbit coupled honeycomb lattice Mott insulators. In
strong $[111]$ magnetic fields that bring the system into the fully polarized
paramagnetic phase, we find that the spin wave bands carry nontrivial Chern
numbers over large regions of the phase diagram implying the presence of chiral
magnon edge states. In contrast to other topological magnon systems, the
topological nontriviality of these systems results from the presence of magnon
number non-conserving terms in the Hamiltonian. Since the effects of
interactions are suppressed by $J/h$, the validity of the single particle
picture is tunable making paramagnetic phases particularly suitable for the
exploration of this physics. Using time dependent DMRG and interacting spin
wave theory, we demonstrate the presence of the chiral edge mode and its
evolution with field.
