  We discuss the potential of using the HeI 584 A forest to detect and study
HeII reionization. Significant 584 A absorption is expected from intergalactic
HeII regions, whereas there should be no detectable absorption from low density
gas in HeIII regions. Unlike HeII Ly-alpha absorption (the subject of much
recent study), the difficulty with using this transition to study HeII
reionization is not saturation but rather that the absorption is weak. The
Gunn-Peterson optical depth for this transition is tau ~ 0.1 x_{HeII} Delta^2
[(1+z)/5]^{9/2}, where x_{HeII} is the fraction of helium in HeII and Delta is
the density in units of the cosmic mean. In addition, HeI 584 A absorption is
contaminated by lower redshift HI Ly-alpha absorption with a comparable flux
decrement. We estimate the requirements for a definitive detection of
redshifted HeI absorption from low density gas (Delta ~ 1), which would
indicate that HeII reionization was occurring. We find that this objective can
be accomplished (using coeval HI Ly-alpha absorption to mask dense regions and
in cross correlation) with a spectral resolution of 10^4 and a signal-to-noise
ratio per resolution element of ~ 10. Such specifications may be achievable on
a few known z ~ 3.5 quasar sightlines with the Cosmic Origins Spectrograph on
the Hubble Space Telescope. We also discuss how HeI absorption can be used to
measure the hardness of the ionizing background above 13.6 eV.
