  Known topological quantum matter, including topological insulators and
Dirac/Weyl semimetals, often hosts robust boundary states in the gaps between
bulk bands in energy-momentum space. Beyond one-gap systems, quantum crystals
may also feature more than one inter-band gap. The manifestation of higher-fold
topology with multiple nontrivial gaps in quantum materials remains elusive. In
this work, we leverage a photoemission spectroscopy probe to discover the
multi-gap topology of a chiral fermion material. We identify two sets of chiral
surface states. These Fermi arcs exhibit an emergent ladder structure in
energy-momentum space, unprecedented in topological materials. Furthermore, we
determine the multi-gap chiral charge $\textbf{C}=(2,2)$. Our results provide a
general framework to explore future complex topological materials.
