  Grand unified theories with fermions transforming as irreducible
representations of a discrete nonabelian flavor symmetry can lead to realistic
fermion masses, without requiring very small fundamental parameters. We
construct a specific example of a supersymmetric GUT based on the flavor
symmetry $\Delta(75)$ --- a subgroup of $SU(3)$ --- which can explain the
observed quark and lepton masses and mixing angles. The model predicts
$\tan\beta \simeq 2-5$ and gives a $\tau$ neutrino mass $m_\nu\simeq M_p/G_F
M_{GUT}^2 = 10$ eV, with other neutrino masses much lighter. Combined
constraints of light quark masses and perturbative unification place flavor
symmetry breaking near the GUT scale; it may be possible to probe these
extremely high energies by continuing the search for flavor changing neutral
currents.
