  We construct a simple and natural supersymmetric model where the dominant
Higgs decay is h -> aa followed by a -> gg. In this case m_h < m_Z is
compatible with all experimental searches, completely eliminating the fine
tuning otherwise required to satisfy Higgs search limits. The model extends the
MSSM with singlet Higgs fields as well as vector-like colored particles that
mediate the decay a -> gg. The a is a pseudo-Nambu Goldstone boson of a new
global U(1) symmetry, and can naturally have any mass from a few GeV to m_h/2.
All interactions can be perturbative up to the GUT scale, and gauge coupling
unification is preserved if the colored mediators come in complete GUT
representations. In this case a -> gamma gamma has a ~1% branching ratio, so h
-> gg gamma gamma may be observable. The colored particles that mediate the h
-> gg decay must be below the TeV scale, and can therefore be produced at the
LHC. If these particles are stable on collider timescales, they will appear as
R-hadrons, a signal visible in early LHC running. A smoking-gun signal that the
stable colored particles are mediators of h -> 4j is R-hadron production in
association with an a. We show that this signal with a -> gamma gamma is
observable at LHC with as little as 10 fb^{-1} of integrated luminosity.
Observation of R-hadrons plus missing energy can show that the superpartner of
the R-hadron is R-parity odd, and therefore not an ordinary quark or gluon.
