Heavy Higgs: Is the Gauge Symmetry Restored in the Early Universe?

The possibility of symmetry non-restoration at high temperature is explored in a strongly interacting Higgs system described by an effective Chiral Lagrangian. Despite a na\"{\i}ve perturbative hint of symmetry non-restoration when the temperature is increased, non-perturbative methods point towards symmetry restoration. (Contribution to the XXXIInd Rencontres de Moriond, "Electroweak Interactions and Unified Theories")