We present a series of high resolution radio and optical observations of the CLASS gravitational lens system B1152+199 obtained with the Multi-Element Radio-Linked Interferometer Network (MERLIN), Very Long Baseline Array (VLBA) and Hubble Space Telescope (HST). Based on the milliarcsecond-scale substructure of the lensed radio components and precise optical astrometry for the lensing galaxy, we construct models for the system and place constraints on the galaxy mass profile. For a single galaxy model with surface mass density Sigma(r) propto r^-beta, we find that 0.95 < beta < 1.21 at 2-sigma confidence. Including a second deflector to represent a possible satellite galaxy of the primary lens leads to slightly steeper mass profiles.