Previous work by the author on diatomic molecules and by others on polyatomic systems has revealed that Kohn-Sham density-functional theory with “gradient corrected” exchangecorrelation approximations gives remarkably good molecular bond and atomization energies. In the present communication, we report the results of an extensive survey of densityfunctional atomization energies on the 55 molecules of the Gaussian-l thermochemical data base of Pople and co-workers [J. Chem. Phys. 90, 5622 ( 1989); 93,2537 ( 1990) 1. These calculations have been performed by the fully numerical molecules (NUMOL) program of Becke and Dickson [J. Chem. Phys. 92,361O ( 1990) ] and are therefore free of basis-set uncertainties. We find an average absolute error in the total atomization energies of our 55 test molecules of 3.7 kcal/mol, compared to 1.6 kcal/mol for the Gaussian-l procedure and 1.2 kcal/mol for Gaussian-2.