  Superluminous supernovae (SLSNe) radiate $\gtrsim 10-100$ times more energy
than ordinary stellar explosions, implicating a novel power source behind these
enigmatic events. One frequently discussed source, particularly for
hydrogen-poor (Type I) SLSNe, is a central engine such as a millisecond
magnetar or accreting black hole. Both black hole and magnetar engines are
expected to channel a fraction of their luminosity into a collimated
relativistic jet. Using 3D relativistic hydrodynamical simulations, we explore
the interaction of a relativistic jet, endowed with a luminosity $L_{\rm
j}\approx10^{45}\,{\rm erg\,s^{-1}}$ and duration $t_{\rm eng} \approx$ days
compatible with those needed to power SLSNe, launched into the envelope of the
exploding star. The jet successfully breaks through the expanding ejecta and
its shocked cocoon powers ultraviolet/optical emission lasting several days
after the explosion and reaching a peak luminosity $\gtrsim 10^{44}$ erg
s$^{-1}$, corresponding to a sizable fraction of $L_{\rm j}$. This high
radiative efficiency is the result of the modest adiabatic losses the cocoon
experiences due to the low optical depths of the enlarged ejecta at these late
times, e.g., compared to the more compact stars in gamma-ray bursts. The
luminosity and temperature of the cocoon emission match those of the ``bumps''
in SLSNe light curves observed weeks prior to the optical maximum in many
SLSNe. Confirmation of jet breakout signatures by future observations (e.g.,
days to weeks-long internal X-ray emission from the jet for on-axis observers,
spectroscopy confirming large photosphere velocities $v/c \gtrsim 0.1$, or
detection of a radio afterglow) would offer strong evidence for central engines
powering SLSNe.
