Using laser light tuned to a repulsive molecular potential, we have been able to suppress inelastic ground-state hyperfine-changing collisions between ultracold {sup 87}Rb atoms. Adiabatic excitation to the repulsive curve alters the atomic trajectories and prevents the atoms from approaching close enough for the hyperfine change to occur. Experimental results show suppressions up to {similar_to}50% and are in reasonable agreement with a simple Landau-Zener model. Our ability to control collisional trap loss processes may have important implications for the achievement of high densities in laser cooled samples.