  It has been realized over the past two decades that topological nontriviality
can be present not only in insulators but also in gapless semimetals, the most
prominent example being Weyl semimetals in three dimensions. Key to topological
classification schemes are the three ``internal" symmetries, time reversal
${\cal T}$, charge conjugation ${\cal C}$, and their product, called chiral
symmetry ${\cal S}={\cal T}{\cal C}$. In this work, we show that robust
topological nodal line semimetal phases occur in $d=3$ in systems whose
internal symmetries include ${\cal S}$, without invoking crystalline symmetries
other than translations. Since the nodal loop semimetal naturally appears as an
intermediate gapless phase between the topological and the trivial insulators,
a sufficient condition for the nodal loop phase to exist is that the symmetry
class must have a nontrivial topological insulator in $d=3$. Our classification
uses the winding number on a loop that links the nodal line. A nonzero winding
number on a nodal loop implies robust gapless drumhead states on the surface
Brillouin zone. We demonstrate how our classification works in all the
nontrivial chiral classes and how it differs from the previous understanding of
topologically protected nodal line semimetals.
