  We examine the performance of a TPC as a gamma-ray telescope above the
pair-creation threshold. The contributions to the photon angular resolution are
studied and their dependence on energy is obtained. The effective area per
detector unit mass for such a thin detector is the conversion mass attenuation
coefficient. The differential sensitivity for the detection of a point-like
source is then derived. Finally, the measurement of track momentum from
deflections due to multiple scattering is optimized.
  These analytical results are exemplified numerically for a few sets of
detector parameters. TPCs show an impressive improvement in sensitivity with
respect to existing pair-creation-based telescopes in the [MeV - GeV] energy
range, even with the modest detector parameters of this study. In addition, gas
TPCs allow an improvement in angular resolution of about one order of
magnitude.
