  We present a supersymmetric extension of the Standard Model with a gauged
SU(2) family symmetry for the leptons. It is shown that this family symmetry
can be consistently broken at the TeV scale along with supersymmetry. If
supersymmetry breaking is driven by anomaly mediation, this model can provide
positive squared masses for the sleptons and thus cure the tachyon problem. We
analyze the constraints and consequences of this scenario. A characteristic
feature of this model is the non-degeneracy of the first two family sleptons.
The model predicts large value of tan(beta) and observable \tau to e \gamma and
B to \mu^+ \mu^- decay rates.
