Vibrational relaxation rate coefficients of naphthalene under collisional assault by argon in a supersonic free jet are reported for the temperature range 1.6-15 K. The rate coefficients are V-T relaxation from the v44′ = 1 level (εvib = 435 cm-1) in electronically excited (1B2u) naphthalene, to the field of destination states that lie within energetic reach, i.e., in the range εvib ≤ 450 cm-1. These data represent the first direct measurement in an S1 polyatomic of the temperature dependence of the absolute magnitude of the vibrational relaxation rate coefficient under conditions of very low energy collisions. The rate coefficient is found to be weakly temperature dependent in the temperature range studied. The temperature dependence of the rate coefficient follows the temperature dependence of the elastic collision rate calculated for particles whose interaction is characterized by the Lennard-Jones 12-6 potential. The vibrational relaxation efficiency, deduced by comparison of the observed relaxation rate with the Lennard-Jones elastic rate, is ≈0.08 at these low temperature. This efficiency is consistent with the expectations based on room temperature data for similar large polyatomics. We conclude that the efficiency of low energy collision induced vibrational relaxation can be explained without invoking assumptions concerning the existence of low-energy resonances in the vibrational relaxation cross section.