Our powder inelastic neutron scattering data indicate that ZnV2O4 is a system of spin chains that are three-dimensionally tangled in the cubic phase above 50 K due to randomly occupied t(2g) orbitals of V3+ (3d(2)) ions. Below 50 K in the tetragonal phase, the chains become straight due to antiferro-orbital ordering. This is evidenced by the characteristic wave vector dependence of the magnetic structure factor that changes from symmetric to asymmetric at the cubic-to-tetragonal transition.