  The symmetry of a material's crystal structure has a significant effect on
the energy states of its electrons. Inversion symmetry, for example, results in
energetically degenerate electron energy bands for electrons with wave vectors
$\textit{k}$ and -$\textit{k}$, but, when spatial inversion symmetry is absent,
this equivalence is no longer possible. In a non-centrosymmetric
superconductor, such inequivalence has an important effect: the standard
superconducting state, where electrons with opposite momenta form pairs on the
Fermi surface, is not possible. A handful of such materials is known; they
display different degrees of influence of this lack of inversion symmetry on
their superconducting properties. The effect of crystal structure chirality on
the properties and applications of superconductors, on the other hand, is
little discussed. Here we report the new isostructural non-centrosymmetric
superconductors TaRh$_2$B$_2$ and NbRh$_2$B$_2$, which have a previously
unreported crystal structure type. Not only do these materials lack inversion
symmetry, but their crystal structure is also chiral; in other words, they can
exist in right-handed or left-handed forms. Unlike most superconductors, their
upper critical magnetic fields extrapolated to 0 K exceed the Pauli limit,
which is often taken as the first indication that a superconducting material is
anomalous. We propose that these materials represent a new kind of platform on
which the effects of handedness on superconductors and their devices can be
tested.
