  We investigate dispersive estimates for the two dimensional Dirac equation
with a potential. In particular, we show that the Dirac evolution satisfies a
$t^{-1}$ decay rate as an operator from the Hardy space $H^1$ to $BMO$, the
space of functions of bounded mean oscillation. This estimate, along with the
$L^2$ conservation law allows one to deduce a family of Strichartz estimates.
We classify the structure of threshold obstructions as being composed of s-wave
resonances, p-wave resonances and eigenfunctions. We show that, as in the case
of the Schr\"odinger evolution, the presence of a threshold s-wave resonance
does not destroy the $t^{-1}$ decay rate. As a consequence of our analysis we
obtain a limiting absorption principle in the neighborhood of the threshold,
and show that there are only finitely many eigenvalues in the spectral gap.
