We report a detailed study of the local composition and structure of a model, bi-phasic nanoglass with nominal stoichiometry Cu55Nb45. Three dimensional atom probe data suggest a nanoscale-phase-separated glassy structure having well defined Cu-rich and Nb-rich regions with a characteristic length scale of ≈ 3 nm. However, extended x-ray absorption fine structure analysis indicates subtle differences in the local environments of Cu and Nb. While the Cu atoms displayed a strong tendency to cluster and negligible structural order beyond the first coordination shell, the Nb atoms had a larger fraction of unlike neighbors (higher chemical order) and a distinctly better-ordered structural environment (higher topological order). This provides the first experimental indication that metallic glass formation may occur due to frustration arising from the competition between chemical ordering and clustering. These observations are complemented by classical as well as ab initio molecular dynamics simulations. Our study indicates that these nanoscale phase-separated glasses are quite distinct from the single phase nanoglasses (studied by Gleiter and others) in the following three respects: (i) they contain at least two structurally and compositionally distinct, nanodispersed, glassy phases, (ii) these phases are separated by comparatively sharp inter-phase boundaries, and (iii) thermally induced crystallization occurs via a complex, multi-step mechanism. Such materials, therefore, appear to constitute a new class of disordered systems that may be called a composite nanoglass.