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 its 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.
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