The spin waves in single crystals of the layered van der Waals antiferromagnet CoPS3 have been measured using inelastic neutron scattering. The data show four distinct spin wave branches with large (>14 meV) energy gaps at the Brillouin zone center indicating significant anisotropy. The data were modeled using linear spin wave theory derived from a Heisenberg Hamiltonian. Exchange interactions up to the third nearest-neighbor in the layered planes were required to fit the data with ferromagnetic J1 = -1.37 meV between first neighbors, antiferromagnetic J3 = 3.0 meV between third neighbors, and a very small J2 = 0.09 meV between second neighbors. A biaxial single-ion anisotropy was required, with a collinear term Dx = -0.77 meV for the axis parallel to the aligned moment direction and a coplanar term Dz = 6.07 meV for an axis approximately normal to the layered crystal planes.