A new class of Cr(V) peroxychromates, those containing waters of hydration (Li 3- CrO 8 .10H 2 O, Na 3 CrO 8 .14H 2 O and Cs 3 CrO 8 .3H 2 O), has been synthesized and characterized by single-crystal X-ray diffraction, magnetic susceptibility, specific heat, and EPR techniques. The Li salt crystallizes into the orthorhombic (Cmcm) group, whereas the Na and Cs salts exhibit the triclinic (P1) and monoclinic P2(1)/n space groups, respectively. Crystal structure analysis indicated the availability of low-dimensional spin-exchange pathways. The orientation dependence of the EPR line width exhibited the (3 cos 2 θ - 1) 4/3 behavior characteristic of linear chain compounds, with θ = 0 coinciding with the chain axis. Correlation of the EPR and X-ray data allowed for the explicit determination of the magnetic chain axes in the crystal and molecular frameworks. Magnetic susceptibility, X , measurements on oriented single crystals yielded negative values for the Curie-Weiss temperatures, indicating dominant antiferromagnetic interactions. The X data yielded the Curie constants that appear to be inversely related to the number of waters of hydration in the crystal structure; this observation is not yet understood. Correlation of the EPR line width, nearest neighbor distances, and Curie constants attested to the essential correctness of the linear chain spin exchange and dipolar fields in the Li and Cs salts, and to a lesser extent also for the Na salt. The specific heat data indicated that all these compounds have the potential to be useful for devices requiring strong heat sinks as well as magnetic refrigerants in the 250 mK temperature regime. They appear to be good as model systems for theoretical investigations on low-dimensional magnetic lattices and for understanding aspects of Cr(VI)-based catalysis and carcinogenesis.