We construct a simple and natural supersymmetric model where the dominant Higgs decay is $h\to aa$ followed by $a\to gg$. 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 minimal supersymmetric standard model with singlet Higgs fields as well as vectorlike colored particles that mediate the decay $a\to gg$. 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 $a\to \gamma \gamma$ has a $\sim 1\%$ branching ratio, so $h\to gg\gamma \gamma$ may be observable. The colored particles that mediate the $a\to gg$ decay must be below the TeV scale, and can therefore be produced at the LHC. If these particles are stable on collider time scales, 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 $h\to 4j$ is $R$-hadron production in association with an $a$. We show that this signal with $a\to \gamma \gamma$ is observable at the LHC with as little as $10{\mathrm{fb}}^{-1}$ of integrated luminosity. Observation of $R$-hadrons plus missing energy would show that the superpartner of the $R$-hadron is $R$-parity odd, and therefore not an ordinary quark or gluon.

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