  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 {\sl 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 $\rm (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 $\rm
(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.
