Solid crystals are defined by a periodic arrangement of atoms in real space, atoms subject to a time-periodic drive can also form crystals in phase space. The interactions between these atoms give rise to collective vibrational modes similar to phonons in solid crystals. The honeycomb phase space crystal is particularly interesting because the vibrational band structure has two sub-lattice bands that can have nontrivial topological physics. The vibrations of any two atoms are coupled via a pairing interaction with intrinsically complex couplings. Their complex phases have a simple geometrical interpretation and can not be eliminated by a gauge transformation, leading to a vibrational band structure with non-trivial Chern numbers and chiral edge states in phase space. In contrast to all topological transport scenarios in real space, the chiral transport for phase space phonons can arise without breaking physical time-reversal symmetry.