Chromium, a transition metal, is one of the important constituents, used widely in steel. It is of paramount importance to study the behavior of hydrogen isotopes with Cr to design a suitable barrier materials for arresting the permeation of H isotopes. Here, the interaction and dynamical behaviours of hydrogen isotopes in bcc Cr lattice have been studied employing plane wave based density functional theory. Nudge elastic band methods have been used to determine the activation energy barrier whereas phonon calculations are performed to calculate the zero point energy in order to investigate the isotope effects. The dissociative surface adsorption of hydrogen is predicted to be exothermic, whereas surface to sub-surface and bulk absorption is found to be endothermic but the vacancy induced absorption energy for H atom in bulk Cr has been found to be exothermic. The diffusion of H atom from one tetrahedral hole to the adjacent tetrahedral hole has been established to be the most favoured pathway. The lighter H atom was shown to have higher diffusion coefficients, permeability coefficients, solubility and rate con- stants than heavier D and T atoms. The computed values of diffusion, permeability and solubility of H in Cr follow the experimental prediction. The computed results presented here might be of assistance in the future design of suitable materials to arrest the permeation of tritium.