Characterising physically realistic spin systems that are useful for quantum computation and also robust to noise is a central problem in quantum information theory. The cluster state in 3-dimensions is the gapped ground state of a local Hamiltonian which exhibits some remarkable properties, including infinite entanglement length at nonzero temperatures [Raussendorf et al. Phys. Rev. A 71, 062313, (2005)]. A natural question to ask is whether there is an ordered phase where some of these properties are insensitive to perturbations. We find a symmetry of the cluster state which puts it in a nontrivial symmetry protected topological (SPT) phase. A consequence of this order is that the ground state of the cluster Hamiltonian retains its infinite entanglement length even when perturbed, provided the perturbations respect the symmetry and are sufficiently small.