  We simulate four flavor noncompact lattice QED using the Hybrid Monte Carlo
algorithm on $10^4$ and $16^4$ lattices. Measurements of the monopole
susceptibility and the percolation order parameter indicate a transition at
$\beta = {1/e^2} = .205(5)$ with critical behavior in the universality class of
four dimensional percolation. We present accurate chiral condensate
measurements and monitor finite size effects carefully. The chiral condensate
data supports the existence of a power-law transition at $\beta = .205$ in the
same universality class as the chiral transition in the two flavor model. The
resulting equation of state predicts the mass ratio $m_\pi^2/m_\sigma^2$ in
good agreement with spectrum calculations while the hypothesis of a
logarithmically improved mean field theory fails qualitatively.
