  We precisely measure the shear viscosity for a resonantly interacting Fermi
gas as a function of temperature, from nearly the ground state through the
superfluid phase transition at a critical temperature $T_c$. Using an iterative
method to invert the data, we extract the {\it local} shear viscosity
coefficient $\alpha_S(\theta)$ versus reduced temperature $\theta$, revealing
previously hidden features. We find that $\alpha_S$ begins to decrease rapidly
with decreasing $\theta$ well above $T_c$, suggesting that preformed pairs play
an important role. Further, we observe that the derivative $\alpha_S'(\theta)$
has a maximum at $T_c$. We compare the local data to several microscopic
theories. Finally, we determine the local ratio of the shear viscosity to the
entropy density.
