  We investigate dispersive estimates for the massless three dimensional Dirac
equation with a potential. In particular, we show that the Dirac evolution
satisfies a $\langle t\rangle^{-1}$ decay rate as an operator from $L^1$ to
$L^\infty$ regardless of the existence of zero energy eigenfunctions. We also
show this decay rate may be improved to $\langle t\rangle ^{-1-\gamma}$ for any
$0\leq \gamma < 1/2$ at the cost of spatial weights. This estimate, along with
the $L^2$ conservation law allows one to deduce a family of Strichartz
estimates in the case of a threshold eigenvalue. We classify the structure of
threshold obstructions as being composed of zero energy eigenfunctions.
Finally, we show the Dirac evolution is bounded for all time with minimal
requirements on the decay of the potential and smoothness of initial data.
