  We report the discovery of the first HeI*\lambda 10830 broad absorption line
quasar FBQS J1151+3822. Using new infrared and optical spectra, as well as the
SDSS spectrum, we extracted the apparent optical depth profiles as a function
of velocity of the 3889A and 10830A HeI* absorption lines. Since these lines
have the same lower levels, inhomogeneous absorption models could be used to
extract the average true HeI* column density; the log of that number was 14.9.
The total hydrogen column density was obtained using Cloudy models. A range of
ionization parameters and densities were allowed, with the lower limit on the
ionization parameter of log U=-1.4 determined by the requirement that there be
sufficient HeI*, and the upper limit on the density of log n=8 determined by
the lack of Balmer absorption. Simulated UV spectra showed that the ionization
parameter could be further constrained in principle using a combination of low
and high ionization lines (such as MgII and PV), but the only density-sensitive
line predicted to be observable and not significantly blended was CIII\lambda
1176. We estimated the outflow rate and kinetic energy, finding them to be
consistent but on the high side compared with analysis of other objects.
Assuming that radiative line driving is the responsible acceleration mechanism,
a force multipler model was constructed. A dynamical argument using the model
results strongly constrained the density to be log n >= ~7. Consequently, the
log hydrogen column density is constrained to be between 21.7 and 22.9, the
mass outflow rate to be between 11 and 56 solar masses per year, the ratio of
the mass outflow rate to the accretion rate to be between 1.2 and 5.8, and the
kinetic energy to be between 1 and 5 x 10^44 erg/s. We discuss the advantages
of using HeI* to detect high-column-density BALQSOs and and measure their
properties. (Abridged)
