  Recent experiments have unveiled important properties of the ground state of
the elusive heavy fermion $\mathrm{URu_{2}Si_{2}}$. While tetragonal
symmetry-breaking was reported below the hidden-order (HO) transition at
$T_{HO}\approx17.5$ K, time-reversal symmetry-breaking was observed below the
superconducting transition temperature $T_{c}<T_{HO}$. Although the latter
results have been used to argue in favor of a chiral $d+id$ superconducting
state, such an order parameter is incompatible with broken tetragonal symmetry.
Here, we employ a phenomenological model to investigate the properties of a
chiral superconducting state that develops inside the hidden-order phase. In
this case, there are actually two superconducting transition temperatures:
while $T_{c}$ marks a normal-state to superconducting transition,
$T_{c}^{*}<T_{c}$ signals a superconducting-to-superconducting transition in
which time-reversal symmetry is broken. In the phase $T_{c}^{*}<T<T_{c}$, the
low-energy density of states $\rho\left(\omega\right)$ is enhanced due to the
crossing of two nodal lines, giving rise to an unusual $\omega\log(\omega)$
dependence of $\rho\left(\omega\right)$, which is manifested in several
thermodynamic properties. We also investigate the emergence of a soft amplitude
gap mode near $T_{c}^{*}$. In contrast to the usual amplitude mode near a
regular normal-state to superconducting transition, this mode becomes soft near
a superconducting-to-superconducting transition, which in principle allows for
its detection by Raman spectroscopy. Finally, we investigate the impact of twin
domains on the anisotropic properties of the superconducting state, and propose
experiments in mechanically strained samples to explore the interplay between
hidden order and superconductivity in $\mathrm{URu_{2}Si_{2}}$.
