  We consider the existence of bulk chiral fermions around points of symmetry
in the Brillouin zone of nonmagnetic 3D crystals with negligible spin-orbit
interactions. We use group theory to show that this is possible, but only for a
reduced number of space groups and points of symmetry that we tabulate.
Moreover, we show that for a handful of space groups the existence of bulk
chiral fermions is not only possible but unavoidable, irrespective of the
concrete crystal structure. Thus our tables can be used to look for bulk chiral
fermions in a specific class of systems, namely that of nonmagnetic 3D crystals
with sufficiently weak spin-orbit coupling. We also discuss the effects of
spin-orbit interactions and possible extensions of our approach to Weyl
semimetals, crystals with magnetic order, and systems with Dirac points with
pseudospin 1 and 3/2. A simple tight-binding model is used to illustrate some
of the issues.
