  We prove spectral and dynamical localization for a one-dimensional Dirac
operator to which is added an ergodic random potential, with a discussion on
the different types of potential. We use scattering properties to prove the
positivity of the Lyapunov exponent through F\"urstenberg theorem. We get then
the H\"older regularity of the integrated density of states through a new
version of Thouless formula, and thus the Wegner estimate necessary for the
multiscale analysis.
