Electron paramagnetic resonance (EPR) of cerium ethyl sulfate (CeES) below 2°K gives evidence of a large nondipolar interaction between nearest-neighbor cerium ions. Writing the spin Hamiltonian for the interaction of two spins Si and Sj as Hij=(αij+Aij)SizSjz+12(βij+Bij)(Si+Sj-+Si-Sj+), where αij and βij are the known contributions from dipole-dipole interaction, the experiments suggest that Aij=0.105+/-0.003 cm-1 and Bij=0.073+/-0.003 cm-1. Although there is no proof, there are four pieces of evidence which strongly support the hypothesis that the interaction is due to electric quadrupole-quadrupole (QQ) interaction. Firstly, the order of magnitude of Aij and Bij are reasonable. Secondly, QQ interaction affords an explanation of the differences between the temperature dependence of the EPR spectra of diluted and undiluted CeES. Thirdly, the spectra of rare-earth impurities in CeES, and fourthly, the spectra of pairs of interacting cerium ions in dilute specimens, are consistent with QQ interaction. Finally, it is shown that superexchange and exchange of virtual phonons probably contribute very little to the observed interaction.