A triplet of EPR lines with a relatively small zero-field splitting and a ratio of peak-to-peak intensities of 1:50:1 was found in lithium niobate crystals grown from the melt, with the addition of potassium and of 1 wt % of Cr. Detailed investigations of the angular dependencies of EPR and electron nuclear double-resonance (ENDOR) spectra, the temperature dependence of EPR spectra, and optical absorption allowed us to attribute this triplet to a family of Cr3+ centers with g = 1.995 +/- 0.005, \b(2)(0)\ approximate to 0.0215 +/- 0.001 cm(-1), and an optical band at 530 nm. Since strong hyperfine interactions of chromium electrons with the nearest Li nuclei were found by ENDOR, it was concluded that Cr in this center substitutes for Nb. Several hydrogen lines were detected in ENDOR spectra. This sheds light on one of the mechanisms of local charge compensation of the centers. The second possible mechanism-charge compensation by additional Li ions in structural vacancies Li-v(+)-is also considered. The members of the family of Cr-Nb centers differ from each other by the location of one or both of these compensating defects. An estimation of crystal-field parameters for the observed low-symmetry exchange pairs in nonstoichiometric crystals shows that they consist of Cr-Li+(3+)-Cr-Li+(3+) centers "glued" by the intrinsic defects, but not of self-compensated Cr-Li+(3+)-Cr-Nb5+(3+) centers.