  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")
