The positively charged state of interstitial chromium in silicon was investigated using electron-nuclear double resonance. We have found the hyperfine interaction of the impurity electrons with nine shells of surrounding silicon neighbors containing 102 atoms. The well-resolved fine structure due to the cubic-field splitting for chromium made it possible to determine the absolute signs of the measured hyperfine interaction parameters. The results are analyzed using a linear combination of atomic orbitals treatment that takes into account the spin S=(5/2 of the impurity and the symmetry of the atomic orbitals centered at the ligands for the different shells. This analysis results in a spin density that is transferred from the impurity to the host crystal of at least 22%. The apparent contradiction between the reduced core polarization (indicating a delocalization of some 52% of the impurity wave function) and the absence of large hyperfine interactions with the silicon ligands is hereby resolved. Our results are compared with those obtained for the positively charged state of interstitial titanium and neutral interstitial iron. It appears that the electronic structure of chromium is similar to that of titanium.