  We prove that the Chern-Simons-Dirac equations in the Coulomb gauge are
locally well-posed from initial data in H^s with s > 1/4 . To study nonlinear
Wave or Dirac equations at this regularity generally requires the presence of
null structure. The novel point here is that we make no use of the null
structure of the system. Instead we exploit the additional elliptic structure
in the Coulomb gauge together with the bilinear Strichartz estimates of
Klainerman-Tataru.
