Hubble Space Telescope V,I photometry of stars in the Large Magellanic Cloud Cluster NGC 1866 shows a well defined cluster main sequence down to V=25 mag, with little contamination from field or foreground stars. We use the main sequence fitting procedure to link the distance of NGC 1866 to the Hipparcos determination of the distance for the Hyades MS stars, making use of evolutionary prescriptions to allow for differences in the chemical composition. On this basis we find a true distance modulus for NGC 1866 of 18.35 +/- 0.05 mag. If the cluster is assumed to lie in the LMC plane then the LMC modulus is 0.02 mag less. ; Comment: ApJL accepted