We prove that any one-ended, locally finite Cayley graph G(Gamma, S), where Gamma is an abelian group and S is a finite generating set of non-torsion elements, admits a decomposition into edge-disjoint Hamiltonian (i.e. spanning) double-rays. In particular, the n-dimensional grid Z(n) admits a decomposition into n edge-disjoint Hamiltonian double-rays for all n is an element of N. (C) 2019 Elsevier Inc. All rights reserved.