We use the Main Sequence stars in the LMC cluster NGC 1866 and of Red Clump stars in the local field to obtain two independent estimates of the LMC distance . We apply an empirical Main Sequence-fitting technique based on a large sample of subdwarfs with accurate Hipparcos parallaxes in order to estimate the cluster distance modulus , and the multicolor Red Clump method to derive distance and reddening of the LMC field . We find that the Main Sequence-fitting and the Red Clump distance moduli are in significant disagreement ; NGC 1866 distance is equal to ( m - M ) _ { 0 ,NGC~ { } 1866 } = 18.33 \pm 0.08 ( consistent with a previous estimate using the same data and theoretical Main Sequence isochrones ) , while the field stars provide ( m - M ) _ { 0 ,field } = 18.53 \pm 0.07 . This difference reflects the more general dichotomy in the LMC distance estimates found in the literature . Various possible causes for this disagreement are explored , with particular attention paid to the still uncertain metallicity of the cluster and the star formation history of the field stars .