We present a detailed powder and single-crystal neutron diffraction study of the spin chain compound Ca3Co2O6. Below 25 K, the system orders magnetically with a modulated partially disordered antiferromagnetic structure. We give a description of the magnetic interactions in the system which is consistent with this magnetic structure. Our study also reveals that the long-range magnetic order coexists with a shorter-range order with a correlation length scale of approximately 180 angstroms in the ab plane. Remarkably, on cooling, the volume of material exhibiting short-range order increases at the expense of the long-range order.