We report measurements of the growth rates of the basal (0 0 0 1) and prism (1 0 (1) over bar 0) facets of ice as a function of surface supersaturation, in a regime where the growth dynamics are dominated by the presence of surface melting. Our measurements were made using freely falling columnar ice crystals, growing a solvent gas of air at a pressure of one atmosphere. with ambient supersaturation levels 1 < (chi) < 11%. Condensation coefficients for the two facets were inferred by modeling the effects of both particle and heat diffusion, which also yielded surface supersaturation levels 0.75 (surf) approximate to 1%. In addition, the condensation coefficient for the basal facet was found to be nearly a factor of 10 larger than for the prism facet. These results support a model in which the ice growth rates are governed by 2D nucleation at the interface between the crystalline solid and a quasi-liquid surface layer.