  The theoretical proposal of chiral fermions in topological semimetals has led
to a significant effort towards their experimental realization. In particular,
the Fermi surfaces of chiral semimetals carry quantized Chern numbers, making
them an attractive platform for the observation of exotic transport and optical
phenomena. While the simplest example of a chiral fermion in condensed matter
is a conventional $|C|=1$ Weyl fermion, recent theoretical works have proposed
a number of unconventional chiral fermions beyond the Standard Model which are
protected by unique combinations of topology and crystalline symmetries.
However, materials candidates for experimentally probing the transport and
response signatures of these unconventional fermions have thus far remained
elusive. In this paper, we propose the RhSi family in space group (SG) $\#$198
as the ideal platform for the experimental examination of unconventional chiral
fermions. We find that RhSi is a filling-enforced semimetal that features near
its Fermi surface a chiral double six-fold-degenerate spin-1 Weyl node at $R$
and a previously uncharacterized four-fold-degenerate chiral fermion at
$\Gamma$. Each unconventional fermion displays Chern number $\pm4$ at the Fermi
level. We also show that RhSi displays the largest possible momentum separation
of compensative chiral fermions, the largest proposed topologically nontrivial
energy window, and the longest possible Fermi arcs on its surface. We conclude
by proposing signatures of an exotic bulk photogalvanic response in RhSi.
