  Black holes are the simplest objects in the universe. They correspond to
extreme deformations of spacetime geometry, and can exist even devoid of
matter. In general relativity, (electro)vacuum black holes are uniquely
determined by their mass, charge and angular momentum. This feature follows
from a uniqueness theorem, which can be evaded if one considers higher
dimensions or matter fields coupled to gravity. Here we find that Einsteinian
cubic gravity, a well-motivated modification of Einstein gravity that includes
third-order curvature corrections in accordance with low-energy effective
theory expectations, admits black hole solutions with charge greater than mass,
when minimally coupled to a Maxwell field. Moreover, we find that, in this
regime, there can be two asymptotically flat black holes with the same charge
and mass, posing the first example of vacuum black hole nonuniqueness in four
dimensions that is free from pathologies. Examination of these black hole's
thermodynamics reveals that when two branches coexist only the larger black
hole is thermodynamically stable, while the smaller branch has negative
specific heat. Einsteinian cubic gravity unveils two further surprising
features. The charged black holes do not possess an inner horizon, in contrast
with the usual Reissner-Nordstr\"om spacetime, thus avoiding the need to resort
to strong cosmic censorship to uphold determinism. In addition to black holes,
there exists a one-parameter family of naked singularity spacetimes sharing the
same mass and charge as the former, but not continuously connected with them.
These naked singularities exist in the under-extremal regime, being present
even in pure (uncharged) Einsteinian cubic gravity.
