  We propose a model in which $A_4$ Family Symmetry arises dynamically from a
six dimensional orbifold SU(5) Supersymmetric Grand Unified Theory. The SU(5)
is broken to the Standard Model gauge group by a particular orbifold
compactification leading to $A_4$ Family Symmetry, low energy Supersymmetry and
Higgs doublet-triplet splitting. The resulting four dimensional effective
superpotential leads to a realistic description of quark and lepton masses and
mixing angles including tri-bimaximal neutrino mixing and an inter-family mass
hierarchy provided by a Froggatt-Nielsen mechanism. This model is the first
which combines the idea of orbifold GUTs with $A_4$ family symmetry resulting
from the orbifolding.
