  During the expansion of a heavy ion collision, the system passes close to the
$O(4)$ critical point of QCD, and thus the fluctuations of the order parameter
$(\sigma, \vec{\pi})$ are expected to be enhanced. Our goal is to compute how
these enhanced fluctuations modify the transport coefficients of QCD near the
pseudo-critical point. We also make a phenomenological estimate for how chiral
fluctuations could effect the momentum spectrum of soft pions.
  We first formulate the appropriate stochastic hydrodynamic equations close to
the $O(4)$ critical point. Then, working in mean field, we determine the
correlation functions of the stress tensor and the currents which result from
this stochastic real time theory, and use these correlation functions to
determine the scaling behavior of the transport coefficients. The hydrodynamic
theory also describes the propagation of pion waves, fixing the scaling
behavior of the dispersion curve of soft pions. We present scaling functions
for the shear viscosity and the charge conductivities near the pseudo-critical
point, and estimate the absolute magnitude of the critical fluctuations to
these parameters and the bulk viscosity.
  Using the calculated pion dispersion curve, we estimate the expected critical
enhancement of soft pion yields, and this estimate provides a plausible
explanation for the excess seen in experiment relative to ordinary hydrodynamic
computations. Our results motivate further phenomenological and numerical work
on the implications of chiral symmetry on real time properties of thermal QCD
near the pseudo-critical point.
