  We demonstrate that a combination of disorder and interactions in a
two-dimensional bulk topological insulator can generically drive its helical
edge insulating. We establish this within the framework of helical Luttinger
liquid theory and exact Emery-Luther mapping. The gapless glassy edge state
spontaneously breaks time-reversal symmetry in a `spin glass' fashion, and may
be viewed as a localized state of solitons which carry half integer charge.
Such a qualitatively distinct edge state provides a simple explanation for
heretofore puzzling experimental observations. This phase exhibits a striking
non-monotonicity, with the edge growing less localized in both the weak and
strong disorder limits.
