We show that arithmetic toral point scatterers in dimension three (“Šeba billiards on R3/ Z3”) exhibit strong level repulsion between the set of “new” eigenvalues. More precisely, let Λ : = { λ1< λ2< … } denote the unfolded set of new eigenvalues. Then, given any γ> 0 , |{i≤N:λi+1-λi≤ϵ}|N=Oγ(ϵ4-γ)as N→ ∞ (and ϵ> 0 small.) To the best of our knowledge, this is the first mathematically rigorous demonstration of a level repulsion phenomena for the quantization of a deterministic system.