  We consider here the class of compact, isolated, high-velocity HI clouds,
CHVCs, which are sharply bounded in angular extent down to a limiting column
density of 1.5x10^18 cm^-2. We describe our automated search algorithm and it's
application to the LDS north of dec= -28 deg. and the HIPASS data south of
dec=0, resulting in an all--sky catalog numbering 246 CHVCs. We argue that
these objects are more likely to represent a single phenomenon in a similar
evolutionary state than would a sample which included any of the major HVC
complexes. Five principal observables are defined for the CHVC population: (1)
the spatial deployment of the objects on the sky, (2) the kinematic
distribution, (3) the number distribution of observed HI column densities, (4)
the number distribution of angular sizes, and (5) the number distribution of
line widths. We show that the spatial and kinematic deployments of the ensemble
of CHVCs contain various clues regarding their characteristic distance. These
clues are not compatible with a location of the ensemble within the Galaxy
proper. The deployments resemble in several regards those of the Local Group
galaxies. We describe a model testing the hypothesis that the CHVCs are a Local
Group population. The agreement of the model with the data is judged by
extracting the observables from simulations, in a manner consistent with the
sensitivities of the observations and explicitly taking account of Galactic
obscuration. We show that models in which the CHVCs are the HI counterparts of
dark-matter halos evolving in the Local Group potential provide a good match to
the observables, if account is taken of tidal and ram--pressure disruption, the
consequences of obscuration due to Galactic HI and of differing sensitivities
and selection effects pertaining to the surveys.
