  The band theory of solids is arguably the most successful theory of condensed
matter physics, providing the description of the electronic energy levels in a
variety of materials. Electronic wavefunctions obtained from the band theory
allow for a topological characterization of the system and the electronic
spectrum may host robust, topologically protected fermionic quasiparticles.
Many of these quasiparticles are analogs of the elementary particles of the
Standard Model, but others do not have a counterpart in relativistic
high-energy theories. A full list of possible quasiparticles in solids is still
unknown, even in the non-interacting case. Here, we report on a new type of
fermionic excitation that appears in metals. This excitation forms a nodal
chain -- a chain of connected loops in momentum space -- along which conduction
and valence band touch. We prove that the nodal chain is topologically distinct
from any other excitation reported before. We discuss the symmetry requirements
for the appearance of this novel excitation and predict that it is realized in
an existing material IrF$_4$, as well as in other compounds of this material
class. Using IrF$_4$ as an example, we provide a detailed discussion of the
topological surface states associated with the nodal chain. Furthermore, we
argue that the presence of the novel quasiparticles results in anomalous
magnetotransport properties, distinct from those of the known materials.
