The coordination environments of Se atoms in binary GexSe100-x, glasses with 5 <= x <= 30 are investigated using a novel, two-dimensional Se-77 nuclear magnetic resonance (NMR) spectroscopic technique. The high-resolution isotropic Se-77 NMR spectra allow for the identification of up to four distinct Se sites in these glasses. The chemical shift tensor parameters for these sites offer unique insights into their local site symmetries and nearest- and next-nearest-neighbor coordination environments. The structural results, when taken together, provide direct evidence in favor of the existence of a randomly connected network of GeSe4 tetrahedra and Se-Se chain fragments in these glasses.