  We examine the possibility that the physical spectrum of a vector-like gauge
field theory exhibits an enhanced global symmetry near a chiral phase
transition. A transition from the Goldstone phase to the symmetric phase is
expected as the number of fermions N_f is increased to some critical value.
Various investigations have suggested that a parity-doubled spectrum develops
as the critical value is approached. Using an effective Lagrangian as a guide,
we note that parity doubling is associated with the appearance of an enhanced
global symmetry in the spectrum of the theory. The enhanced symmetry would
develop as the spectrum splits into two sectors, with the first exhibiting the
usual pattern of a spontaneously broken chiral symmetry, and the second
exhibiting an additional, unbroken symmetry and parity doubling. The first
sector includes the Goldstone bosons and other states such as massive scalar
partners. The second includes a parity-degenerate vector and axial vector along
with other possible parity partners. We note that if such a near-critical
theory describes symmetry breaking in the electroweak theory, the additional
symmetry suppresses the contribution of the parity doubled sector to the S
parameter.
