  We present a calculable supersymmetric theory of a composite ``fat'' Higgs
boson. Electroweak symmetry is broken dynamically through a new gauge
interaction that becomes strong at an intermediate scale. The Higgs mass can
easily be 200-450 GeV along with the superpartner masses, solving the
supersymmetric little hierarchy problem. We explicitly verify that the model is
consistent with precision electroweak data without fine-tuning. Gauge coupling
unification can be maintained despite the inherently strong dynamics involved
in electroweak symmetry breaking. Supersymmetrizing the Standard Model
therefore does not imply a light Higgs mass, contrary to the lore in the
literature. The Higgs sector of the minimal Fat Higgs model has a mass spectrum
that is distinctly different from the Minimal Supersymmetric Standard Model.
