The short-range structure, connectivity, and chemical order in AsxTe100-x (25 <= x <= 65) glasses are studied using high-resolution two-dimensional projection magic-angle-turning (pjMAT) Te-125 nuclear magnetic resonance (NMR) spectroscopy. The Te-125 pjMAT NMR results indicate that the coordination of Te atoms obeys the 8-N coordination rule over the entire composition range. However, in strong contrast with the analogous glass-forming As-S and As-Se chalcogenides, significant violation of chemical order is observed in As-Te glasses over the entire composition range in the form of homopolar As-As (Te-Te) bonds, even in severely As (Te)-deficient glasses. The speciation of the Te coordination environments can be explained with the dissociation reaction model As2Te3 -> 2As + 3Te(II), characterized by a dissociation constant that is independent of glass composition. These structural characteristics can be attributed to the high metallicity of Te and the strong energetic similarity between the Te-Te, Te-As, and As-As bonds, and they are consistent with the monotonic and often nearly linear variation of physical properties observed in telluride glasses as a function of the Te content.