Bound optical phonons associated with the phonon-assisted I1 (4888 Å) transition in CdS have been observed. These states arise from the bonding of an LO phonon to a neutral acceptor, which provides an attractive interaction for the phonon. The interaction is with LO phonons of small wave vector (near k-->=0). Both the Γ1 and Γ5 LO phonons, which result from a splitting due to anisotropic short-range interatomic forces, are observed in the bound states. The optical transitions described in this paper are similar to those described by Dean et al., which involved optical phonons bound to neutral donors in GaP. The observed bound states were identified as 2S, 2P, and 3D states with measured binding energies of 26.4, 21.6, and 11.6 cm-1, respectively.