  More than half a century ago Penrose asked: are the superfluid and solid
state of matter mutually exclusive or do there exist "supersolid" materials
where the atoms form a regular lattice and simultaneously flow without
friction? Recent experiments provide evidence that supersolid behavior indeed
exists in Helium-4 -- the most quantum material known in Nature. In this paper
we show that large local strain in the vicinity of crystalline defects is the
origin of supersolidity in Helium-4. Although ideal crystals of Helium-4 are
not supersolid, the gap for vacancy creation closes when applying a moderate
stress. While a homogeneous system simply becomes unstable at this point, the
stressed core of crystalline defects (dislocations and grain boundaries)
undergoes a radical transformation and can become superfluid.
