A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the dynamics of the spin and the chirality flips. The problems to overcome in order to find a c-number path integral representation for the solution of the Dirac equation i¯h∂tΨ = HΨ = [ (−ic¯h ∂ + eA) · α + mc 2 β − eV] Ψ (1) is (i) to generate the first order derivatives in the space coordinates and (ii) to treat the spinor indices. The traditional method to tackle these problems is to use space-time lattice and sum over the lattice trajectories [1], and the application of Grassman variables [2]. The inherent limitation of this solution lies in the difficulty in arriving at the propagation in continuous space and in developing analytic non-perturbative approximations. We present