We analyse the stellar kinematics of the z = 0.169 brightest cluster galaxy ( BCG ) in Abell 120 , using integral field observations with VLT/MUSE . This galaxy has a gravitationally-lensed arc located at unusually small radius ( \sim 5 kpc ) , allowing us to constrain the mass distribution using lensing and stellar dynamical information over the same radial range . We measure a velocity dispersion profile which is nearly flat at \sigma \approx 285 km s ^ { -1 } in the inner \sim 5 kpc , and then rises steadily to \sigma \approx 360 km s ^ { -1 } at \sim 30 kpc . We analyse the kinematics using axisymmetric Jeans models , finding that the data require both a significant dark matter halo ( to fit the rising outer profile ) and a compact central component , with mass M _ { cen } \approx 2.5 \times 10 ^ { 10 } M _ { \odot } ( to fit the flat \sigma in the inner regions ) . The latter component could represent a super-massive black hole , in which case it would be among the largest known to date . Alternatively M _ { cen } could describe excess mass associated with a gradient in the stellar mass-to-light ratio . Imposing a standard NFW dark matter density profile , we recover a stellar mass-to-light ratio \Upsilon which is consistent with a Milky-Way-like initial mass function ( IMF ) . By anchoring the models using the lensing mass constraint , we break the degeneracy between \Upsilon and the inner slope \gamma of the dark matter profile , finding \gamma = 1.0 \pm 0.1 , consistent with the NFW form . We show that our results are quite sensitive to the treatment of the central mass in the models . Neglecting M _ { cen } biases the results towards both a heavier-than-Salpeter IMF and a shallower-than-NFW dark matter slope ( \gamma \approx 0.5 ) .