Topological semimetals in crystals with a chiral structure (which possess a handedness due to a lack of mirror and inversion symmetries) are expected to display numerous exotic physical phenomena, including fermionic excitations with large topological charge, long Fermi arc surface states unusual magnetotransport and lattice dynamics, as well as a quantized response to circularly polarized light. So far, all experimentally confirmed topological semimetals exist in crystals that contain mirror operations, meaning that these properties do not appear. Here, we show that AlPt is a structurally chiral topological semimetal that hosts new four-fold and six-fold fermions, which can be viewed as a higher spin generalization of Weyl fermions without equivalence in elementary particle physics. These multifold fermions are located at high symmetry points and have Chern numbers larger than those in Weyl semimetals, thus resulting in multiple Fermi arcs that span the full diagonal of the surface Brillouin zone. By imaging these long Fermi arcs, we experimentally determine the magnitude and sign of their Chern number, allowing us to relate their dispersion to the handedness of their host crystal.