Chirality-the geometric property of objects that do not coincide with their mirror image-is found in nature, for example, in molecules, crystals, galaxies and life forms. In quantum field theory, the chirality of a massless particle is defined by whether the directions of its spin and motion are parallel or antiparallel. Although massless chiral fermions-Weyl fermions-were predicted 90 years ago, their existence as fundamental particles has not been experimentally confirmed. However, their analogues have been observed as quasiparticles in condensed matter systems. In addition to Weyl fermions1-4, theorists have proposed a number of unconventional (that is, beyond the standard model) chiral fermions in condensed matter systems5-8, but direct experimental evidence of their existence is still lacking. Here, by using angle-resolved photoemission spectroscopy, we reveal two types of unconventional chiral fermion-spin-1 and charge-2 fermions-at the band-crossing points near the Fermi level in CoSi. The projections of these chiral fermions on the (001) surface are connected by giant Fermi arcs traversing the entire surface Brillouin zone. These chiral fermions are enforced at the centre or corner of the bulk Brillouin zone by the crystal symmetries, making CoSi a system with only one pair of chiral nodes with large separation in momentum space and extremely long surface Fermi arcs, in sharp contrast to Weyl semimetals, which have multiple pairs of Weyl nodes with small separation. Our results confirm the existence of unconventional chiral fermions and provide a platform for exploring the physical properties associated with chiral fermions.