  We perform a real-time simulation of the $O(4)$ critical point of QCD, which
lies in the dynamic universality class of Model G. The axial charge and the
order parameter $\phi_a =(\sigma, \vec{\pi})$ exhibit a rich dynamical
interplay, which reflects the qualitative differences in the hydrodynamic
effective theories above and below $T_c$. From the axial charge correlators on
the critical line we extract a dynamical critical exponent of $\zeta=1.47 \pm
0.01 ({\rm stat})$, which is compatible with the theoretical expectation of
$\zeta = d/2$ (with $d=3$) when systematic errors are taken into account. At
low temperatures, we quantitatively match the $O(4)$ simulations to the
superfluid effective theory of soft pions.
