  We consider triple Higgs boson production at a future 100 TeV proton-proton
collider. We perform a survey of viable final states and compare and contrast
triple production to Higgs boson pair production. Focussing on the $hhh
\rightarrow (b\bar{b}) (b\bar{b}) (\gamma \gamma)$ final state, we construct a
baseline analysis for the Standard Model scenario and simple deformations,
demonstrating that the process merits investigation in the high-luminosity
phase of the future collider as a new probe of the self-coupling sector of the
Higgs boson.
