We present stellar kinematics and orbit superposition models for the central regions of four Brightest Cluster Galaxies ( BCGs ) , based upon integral-field spectroscopy at Gemini , Keck , and McDonald Observatories . Our integral-field data span radii from < 100 pc to tens of kiloparsecs , comparable to the effective radius of each galaxy . We report black hole masses , M _ { \bullet } , of 2.1 ^ { +1.6 } _ { -1.6 } \times 10 ^ { 10 } M _ { \odot } for NGC 4889 , 9.7 ^ { +3.0 } _ { -2.5 } \times 10 ^ { 9 } M _ { \odot } for NGC 3842 , and 1.3 ^ { +0.5 } _ { -0.4 } \times 10 ^ { 9 } M _ { \odot } for NGC 7768 , with errors representing 68 \% confidence limits . For NGC 2832 we report an upper limit of M _ { \bullet } < 9.0 \times 10 ^ { 9 } M _ { \odot } . Our models of each galaxy include a dark matter halo , and we have tested the dependence of M _ { \bullet } on the model dark matter profile . Stellar orbits near the center of each galaxy are tangentially biased , on comparable spatial scales to the galaxies ’ photometric cores . We find possible photometric and kinematic evidence for an eccentric torus of stars in NGC 4889 , with a radius of nearly 1 kpc . We compare our measurements of M _ { \bullet } to the predicted black hole masses from various fits to the relations between M _ { \bullet } and stellar velocity dispersion ( \sigma ) , luminosity ( L ) , or stellar mass ( M _ { \star } ) . Still , the black holes in NGC 4889 and NGC 3842 are significantly more massive than all \sigma -based predictions and most L -based predictions . The black hole in NGC 7768 is consistent with a broader range of predictions .