  Topological semimetals in three dimensions display band-touchings at points
(Weyl or Dirac semimetals) or nodal lines in the Brillouin zone. Weyl
semimetals can occur with internal symmetries only (time-reversal ${\cal T}$,
charge conjugation ${\cal C}$, and a product of the two, called
chiral/sublattice symmetry ${\cal S}={\cal T}{\cal C}$). Nodal line semimetals
possessing solely internal symmetries have only been classified abstractly,
while those with SU(2) spin rotation or crystalline symmetries are known more
explicitly. We show that chiral symmetry classes that are topologically
nontrivial in three dimensions (namely class AIII, CII, CI, and DIII) always
have a stable gapless phase, which is a topological nodal line semimetal. Our
classification differs from previous approaches and has direct implications for
gapless surface states.
