  The concept of a supersolid state is paradoxical. It combines the
crystallization of a many-body system with dissipationless flow of the atoms it
is built of. This quantum phase requires the breaking of two continuous
symmetries, the phase invariance of a superfluid and the continuous
translational invariance to form the crystal,. Proposed for helium almost 50
years ago, experimental verification of supersolidity remains elusive. A
variant with only discrete translational symmetry breaking on a preimposed
lattice structure, the `lattice supersolid', has been realized based on
self-organization of a Bose-Einstein condensate (BEC). However, lattice
supersolids do not feature the continuous ground state degeneracy that
characterizes the supersolid state as originally proposed. Here we report the
realization of a supersolid with continuous translational symmetry breaking.
The continuous symmetry emerges from two discrete spatial ones by symmetrically
coupling a BEC to the modes of two optical cavities. We establish the phase
coherence of the supersolid and find a high ground-state degeneracy by
measuring the crystal position over many realizations through the light fields
leaking from the cavities. These light fields are also used to monitor the
position fluctuations in real-time. Our concept provides a route to creating
and studying glassy many-body systems with contrallably lifted ground-state
degeneracies, such as supersolids in the presence of disorder.
