  We explore the possibility of explaining the recent $\sim 750$ GeV excesses
observed by ATLAS and CMS in the $\gamma\gamma$ spectrum in the context of a
compelling theory of Naturalness. The potential spin-zero resonance responsible
for the excesses also requires the existence of new heavy charged states. We
show that both such features are naturally realized in a see-saw Composite
Higgs model for EWSB, where the new pseudo-Goldstone bosons are expected to be
comparatively heavier than the SM Higgs, and the new fermions have masses in
the TeV range. If confirmed, the existence of this new resonance could be the
first stone in the construction of a new theory of Naturalness.
