  Positronium is the short-lived atom consisting of a bound electron-positron
pair. In the triplet state, when the spins of both particles are parallel,
radiative recombination lines will be emitted prior to annihilation. The
existence of celestial positronium is revealed through gamma-ray observations
of its annihilation products. These observations however have intrinsically low
angular resolution. In this paper we examine the prospects for detecting the
positronium recombination spectrum. Such observations have the potential to
reveal discrete sources of positrons for the first time and will allow the
acuity of optical telescopes and instrumentation to be applied to observations
of high energy phenomena.
  We review the theory of the positronium recombination spectrum and provide
formulae to calculate expected line strengths from the positrons production
rate and for different conditions in the interstellar medium. We estimate the
positronium emission line strengths for several classes of Galactic and
extragalactic sources. These are compared to current observational limits and
to current and future sensitivities of optical and infrared instrumentation. We
find that observations of the Ps-alpha line should soon be possible due to
recent advances in near-infrared spectroscopy.
