The chemical enthalpies of formation of the liquid alloy, ∆Hc,l, of Cu–Zr-rich Cu–Zr–Al bulk metallic glasses (BMGs) in a broad composition region have been calculated, in order—to investigate the effect of the chemical bonding on the thermal stability of these BMGs, based on the efficient cluster-packing model. It is found that the Al–Zr bonding has more important effect than the Cu–Zr bonding on the thermal stability of Cu–Zr-rich Cu–Zr–Al BMGs with the same Cu/Zr content ratio, and the thermal stability of Cu–Zr-rich Cu–Zr–Al BMGs has close correlation with the chemical stability. The results could be useful for understanding the underlying mechanism of crystallization of metallic glasses.