  We report the detection of a deep broad HI 21 cm absorption system at z =
0.78 toward the radio source [HB89] 2351+456 (4C+45.51) at z = 1.992. The HI
absorption was identified in a blind spectral line survey conducted at the
Green Bank Telescope spanning 0.63 < z < 1.10 toward a large sample of radio
continuum sources. The HI column density is N(HI) = 2.35 x 10^19 (T_s/f) cm^-2,
where T_s is the spin temperature and f is the continuum covering factor of the
absorbing gas. For T_s/f > 8.5 K, this system is by definition a damped Ly
alpha absorption system (N(HI) >= 2 x 10^20 cm^-2). The line is unusually
broad, with a FWHM of 53 km/s and a full span of 163 km/s, suggesting a
physically extended HI gas structure. Radio surveys identify damped Ly alpha
systems in a manner that bypasses many of the selection effects present in
optical/UV surveys, including dust extinction and the atmospheric cutoff for z
< 1.65. The smooth broad profile of this HI 21 cm absorption system is similar
to the z = 0.89 HI absorption toward PKS 1830-211, which suggests that the
absorber toward [HB89] 2351+456 is also a gravitational lens and a molecular
absorption system. However, very long baseline interferometry and Hubble Space
Telescope observations show little evidence for gravitational lensing, and BIMA
millimeter observations show no HCO+ (1-2) or HCN (1-2) absorption down to tau
= 0.15 (3 sigma) in 5 km/s channels. Although this radio damped Ly alpha
selection technique would include dusty, molecule-rich systems, [HB89] 2351+456
appears to be a ``vanilla'' HI 21 cm absorber.
