  We have determined the location of the line-opacity modified Eddington limit
for stars in the LMC using the most recent atmosphere models combined with a
precise mapping to the HR Diagram through up-to-date stellar evolution
calculations. While we find, in agreement with previous studies, that the shape
of the modified Eddington limit qualitatively corresponds to the
Humphreys-Davidson (HD) limit defined by the most luminous supergiants, the
modified limit is actually a full magnitude higher than the upper luminosity
limit observed for LMC stars. The observed limit is consistent with atmosphere
models in which the maximum value of the ratio of the radiation force outwards
to the gravitational force inwards, Y_max, is 0.9, i.e., the photospheres of
stars at the observed luminosity limit are bound. As massive stars evolve, they
move to higher, and therefore less stable values of Y_max, so mass loss, either
sporadic or continuous, may halt their natural redward evolution as they
approach the Y_max = 0.9 limit. We assess the metallicity dependence of this
limit. If the limit does determine the most luminous stars, and the value of
Y_max corresponding to the luminosity limit in the LMC is universal, then the
brightest supergiants the SMC should be only marginally brighter (0.3 mag) than
those of the LMC, in agreement with observations. Moreover, the brightest
supergiants in M31 should be 0.75~mag fainter than those in the LMC.
