  We propose a new scenario for solving the tachyonic slepton mass problem of
anomaly mediated supersymmetry breaking models with a non-Abelian horizontal
gauge symmetry broken at the TeV scale. A specific model based on SU(3)_{H}
horizontal symmetry is presented wherein the sleptons receive positive
mass-squared from the asymptotically free SU(3)_{H} gauge sector. Approximate
global symmetries present in the model strongly suppress flavor changing
processes induced by the horizontal vector gauge bosons. The model predicts
m_{h} < 120 GeV for the lightest Higgs boson mass, tan{beta} nearly equal to 4,
and M_V = 1-4 TeV for the SU(3)_{H} gauge boson masses. The lightest SUSY
particle is found to be the neutral Wino, which is a candidate for cold dark
matter.
