The possibility that the Galactic spheroid was assembled from isolated, chemically distinct proto-Galactic fragments is investigated using a Monte Carlo technique designed to simulate the chemical evolution of the Galaxy in hierarchical formation scenarios which involve no gas dissipation. By comparing the observed and simulated metallicity distributions of Galactic globular clusters and halo field stars, we estimate the level of fragmentation in the collapsing proto-Galaxy. Although the formation process is highly stochastic, the simulations frequently show good agreement with the observed metallicity distributions, provided the luminosity function of proto-Galactic fragments had the form dN L^α dL, where α ~ -2. While this steep slope is strongly at odds with the presently observed luminosity function of the Local Group, it is in close agreement with the predictions of semianalytic and numerical models of hierarchical galaxy formation. We discuss a number of possible explanations for this discrepancy. These simulations suggest that the Galactic halo and its globular cluster system were assembled via the accretion and disruption of ~10³ metal-poor, proto-Galactic fragments by the dominant building block: a protobulge whose own metal-rich globular clusters system has been preferentially eroded by dynamical processes. This formation scenario may provide a simple explanation for the different shapes of the Galactic globular cluster and halo star metallicity distributions. Based on the similar properties of globular clusters belonging to spiral and giant elliptical galaxies, we argue that the same process (e.g., hierarchical growth involving little gas dissipation) is responsible for the formation of both giant elliptical galaxies and the bulge-halo components of spiral galaxies.