Contributions to the first-order rate constant for the decay of the Eu3+(D-5(0)) state of tris(2,2,6,6-tetramethyl-3,5-heptanedionato)europium(III), Eu(thd)(3), from radiative and multiphonon mechanisms are evaluated independently by measuring the luminescence decay rates in undeuterated Eu(thd)(3), fully deuterated Eu(thd-d(19))(3), and alpha-deuterated Eu(thd-d(1))(3), which is also designated Eu(alpha-D,thd)(3). In the latter case, deuterium substitution is at the alpha-carbon, between the carbonyl groups of the beta-diketonate ligand. These measurements yield a multiphonon contribution of 332 s(-1), of which 157 s(-1) is attributed to relaxation via the C-alpha-H stretching vibration and 175 s(-1) to relaxation via the C-H stretching modes of the tert-butyl groups. By use of the measured total Eu3+(D-5(0)) relaxation rate constant and the multiphonon rate constants given above, the Eu3+(D-5(0)) radiative relaxation rate constant is inferred to be 1930 s(-1). It is suggested that this unusually high radiative rate constant may be due to an increased allowedness in the D-5(0) --> F-7(J) transitions due to contributions to the predominantly 4f crystal-field wave functions from a low-lying ligand-to-metal charge-transfer state.