The absorption spectrum of H219O, a radioactive isotopologue of the water molecule, is predicted using variational nuclear motion calculated based on a high precision potential energy function and ab initio dipole moment surface. Vibrational - rotational energy levels and wave functions, line centers and Einstein coefficients for dipole transitions are calculated. Predicted transition wavenumbers are improved by extrapolating known empirical energy levels of the stable H216O, H217O and H218O isotopologues to H219O. A line list for possible atmospheric application is presented which includes air line broadening coefficients. The calculations span a wide spectral range covering infrared and visible wavelengths, and are appropriate for temperatures up to 1000 K. Windows suitable for observing absorption by H219O are identified and comparisons made with the infrared spectra of water vapor in natural abundance, H215O and H214O.