We consider the form of the chiral-symmetry-breaking piece of the effective potential in the linear σ model. Surprisingly, it allows for a second local minimum at both zero and finite temperatures. Even though chiral symmetry is not exact, and therefore is not restored in a true phase transition at finite temperature, this second minimum can nevertheless mimic many of the effects of a first-order phase transition. We derive a lower limit on the height of the second minimum relative to the global minimum based on cosmological considerations; this limit is so weak as to be practically nonexistent. In high energy nuclear collisions, it may lead to observable effects in Bose-Einstein interferometry due to domain walls and to coherent pion emission.