  Precision cosmology requires accurate galaxy redshifts, but next generation
optical surveys will observe unprecedented numbers of resolved galaxies,
placing strain on the amount of spectroscopic follow-up required. We show how
useful information can be gained on the redshift distributions of optical
galaxy samples from spatial cross-correlations with intensity maps of
unresolved HI (21cm) spectral line emission. We construct a redshift
distribution estimator, which we test using simulations. We utilise the S3-SAX
catalogue which includes HI emission information for each galaxy, which we use
to construct HI intensity maps. We also make use of simulated LSST and
Euclid-like photometry enabling us to apply the HI clustering calibration to
realistic simulated photometric redshifts. While taking into account important
limitations to HI intensity mapping such as lost k-modes from foreground
cleaning and poor angular resolution due to large receiver beams, we show that
excellent constraints on redshift distributions can be provided for an optical
photometric sample.
