Chiral four-spin exchange generates a momentum-dependent magnon spin in a compensated honeycomb antiferromagnet at zero magnetic field. For a Néel vector tilted by an angle θ₀ from the layer normal, the interaction contributes to intersublattice magnon pairing already at harmonic order, with an amplitude proportional to cosθ₀sin²θ₀. Biaxial anisotropy mixes the two longitudinal-spin sectors, producing nonquantized mode spins that are odd in momentum, while a sublattice-exchange relation keeps the magnon energies reciprocal. A temperature gradient then induces a spin density along the Néel axis through a redistribution of magnon occupations. Reversing the four-spin coupling reverses this spin density and the mode spins without changing the magnon energies. MnPS₃ motivates the magnetic geometry; realizing the interaction requires a structural modification compatible with the symmetry assumptions of the model.