We present Hubble Space Telescope photometry for three fields in the o
uter disk of the Large Magellanic Cloud (LMC) extending approximately
4 mag below the faintest main-sequence turnoff. We cannot detect any s
trongly significant differences in the stellar populations of the thre
e fields based on the morphologies of the color-magnitude diagrams, th
e luminosity functions, and the relative numbers of stars in different
evolutionary stages. Our observations therefore suggest similar star
formation histories in these regions, although some variations are cer
tainly allowed. The fields are located in two regions of the LMC: one
is in the northeast and two are located in the northwest. Under the as
sumption of a common star formation history, we combine the three fiel
ds with ground-based data at the same location as one of the fields to
improve statistics for the brightest stars. We compare this stellar p
opulation with those predicted from several simple star formation hist
ories suggested in the literature, using a combination of the R-method
of Bertelli et al. (1992) and comparisons with the observed luminosit
y function. The only model we consider that is not rejected by the obs
ervations is one in which the star formation rate is roughly constant
for most of the LMC's history and then increases by a factor of 3 abou
t 2 Gyr ago. Such a model has roughly equal numbers of stars older and
younger than 4 Gyr, and thus is not dominated by young stars. This st
ar formation history, combined with a closed-box chemical evolution mo
del, is consistent with observations that the metallicity of the LMC h
as doubled in the past 2 Gyr.