I will report theory and simulations of the continuum equations for a droplet of active polar liquid crystal. These equations offers a simple representation of a cell extract", such a droplet of actomyosin solution, in which myosin motors moving on actin filaments create internal stresses as a result of biological activity. (This system can in turn be viewed as a stripped-down representation of the cytoskeleton which causes locomotion of eukarotic cells.) Actomyosin is an active liquid crystal whose polarity describes the mean sense of alignment of actin fibres. In the absence of polymerization and depolymerization processes (`treadmilling') which arise respectively at the plus and minus ends of the filaments, the active dynamics should be unchanged when polarity is reversed. Our results suggest that, contrary to most literature opinion, locomotion can arise in the absence of treadmilling, by spontaneous symmetry breaking (SSB) of polarity inversion symmetry.