We present near-infrared integral field spectroscopy of the central kiloparsec of NGC 1275 at the heart of the Perseus cluster of galaxies , obtained with the UIST IFU on UKIRT . The nuclear ro-vibrational H _ { 2 } emission is spatially resolved and is likely to originate approximately 50 pc from the active nucleus . The Pa \alpha emission is , by contrast , spatially unresolved . The requirements for thermal excitation of the H _ { 2 } by nuclear X-radiation , its kinematics on sub-arcsec scales , and its stability against self-gravity , together suggest that the observed H _ { 2 } is part of clumpy disk rotating about the radio-jet axis . The sharp jump in the H _ { 2 } velocity across the nucleus implies a black hole mass of 3.4 \times 10 ^ { 8 } \thinspace M _ { \odot } , with a systematic error of \pm 0.18 dex due to the uncertainty in the radio jet inclination . This agrees well with the value implied by the empirical correlation between black hole mass and stellar velocity dispersion for nearby elliptical galaxies , and is \sim 100 times the stellar mass in this region .