  Supersolid is a mysterious and puzzling state of matter whose possible
existence has stirred a vigorous debate among physicists for over 60 years. Its
elusive nature stems from the coexistence of two seemingly contradicting
properties, long-range order and superfluidity. We report computational
evidence of a supersolid phase of deuterium under high pressure ($p >800$ GPa)
and low temperature (T $<$ 1.0 K). In our simulations, that are based on
bosonic path integral molecular dynamics, we observe a highly concerted
exchange of atoms while the system preserves its crystalline order. The
exchange processes are favoured by the soft core interactions between deuterium
atoms that form a densely packed metallic solid. At the zero temperature limit,
Bose-Einstein condensation is observed as the permutation probability of $N$
deuterium atoms approaches $1/N$ with a finite superfluid fraction. Our study
provides concrete evidence for the existence of a supersolid phase in
high-pressure deuterium and could provide insights on the future investigation
of supersolid phases in real materials.
