Using single crystal inelastic neutron scattering with and without the application of an external magnetic field and powder neutron diffraction, we have characterized magnetic interactions in Ba3Cr2O8. Even without a field, we found that there exist three singlet-to-triplet excitation modes in the (h, h, l) scattering plane. Our complete analysis shows that the three modes are due to spatially anisotropic interdimer interactions that are induced by lattice distortions of the tetrahedron of oxygens surrounding the Jahn-Teller active Cr5+(3d1). The strong intradimer coupling of J0=2.38(2) meV and weak interdimer interactions (|Jinter|< or =0.52(2) meV) makes Ba3Cr2O8 a good model system for weakly coupled s=1/2 quantum spin dimers.