  We show that edges of Quantum Spin Hall topological insulators represent a
natural platform for realization of exotic supersolid phase. On one hand,
fermionic edge modes are helical due to the nontrivial topology of the bulk. On
the other hand, a disorder at the edge or magnetic adatoms may produce a dense
array of localized spins interacting with the helical electrons. The spin
subsystem is magnetically frustrated since the indirect exchange favors
formation of helical spin order and the direct one favors (anti)ferromagnetic
ordering of the spins. At a moderately strong direct exchange, the competition
between these spin interactions results in the spontaneous breaking of parity
and in the Ising type order of the $z$-components at zero temperature. If the
total spin is conserved the spin order does not pin a collective massless
helical mode which supports the ideal transport. In this case, the phase
transition converts the helical spin order to the order of a chiral lattice
supersolid. This represents a radically new possibility for experimental
studies of the elusive supersolidity.
