Although the crystal field has a strong influence on the heavy fermion properties of CeAl{sub 3}, the parameters of the crystal field Hamiltonian have not been established. We present the results of an analysis of inelastic neutron scattering data on CeAl{sub 3} to resolve this issue. By combining the neutron scattering results with measurements of the single crystal magnetic susceptibility, we have obtained an unambiguous set of crystal field parameters in CeAl{sub 3}: B{sub 2}{sup 0} = (5.8 {+-} 0.2) x 10{sup {minus}2} meV and B{sub 4}{sup 0} = (2.3 {+-} 0.1) x 10{sup {minus}2} meV. The corresponding level scheme of the ground multiplet of the Ce{sup 3+} ion is characterized by a {Lambda}{sub 9} {vert_bar} {+-} 3/2> ground state doublet and two close-lying excited doublets {Lambda}{sub 8} {vert_bar} {+-} 5/2> and {Lambda}{sub 7} {vert_bar} {+-} 1/2> at an energy of {approximately} 6.4 meV at 20 K. A comparison of the crystal field parameters along the RAl{sub 3} (R = Ce, Pr and Nd) series of isostructural compounds shows that in CeAl{sub 3}, A{sub 2}{sup 0} is an order of magnitude larger, and A{sub 4}{sup 0} is three times larger, than in PrAl{sub 3} and NdAl{sub 3}. These increases cannot be explained by changes in lattice parameters but are more likely to result from the enhancement of the hybridization of the cerium 4f electrons with the conduction electrons in CeAl{sub 3}. This conclusion is in an agreement with the results of our study of the RCu{sub 2}Si{sub 2} series.