Approximate Truncated Schwinger-Dyson methods have predicted that
when massless QED is subjected to strong external magnetic fields, chiral
symmetry, which is a good symmetry for massless QED without these external
fields, is broken. We use Rational Hybrid Monte Carlo (RHMC) simulations to
study lattice QED in a strong constant homogeneous external magnetic field.
We use the chiral condensate $\langle\bar{\psi}\psi\rangle$ as an order
parameter for chiral symmetry breaking. A non-zero value of this condensate
in the limit of zero mass electrons in a strong magnetic field indicates that
the magnetic field does break chiral symmetry.