  We present deep Hubble Space Telescope (HST) NICMOS 2 F160W band observations
of the central 56*57" (14pc*14.25pc) region around R136 in the starburst
cluster 30 Dor (NGC 2070) located in the Large Magellanic Cloud. Our aim is to
derive the stellar Initial Mass Function (IMF) down to ~1 Msun in order to test
whether the IMF in a massive metal-poor cluster is similar to that observed in
nearby young clusters and the field in our Galaxy. We estimate the mean age of
the cluster to be 3 Myr by combining our F160W photometry with previously
obtained HST WFPC2 optical F555W and F814W band photometry and comparing the
stellar locus in the color-magnitude diagram with main sequence and pre-main
sequence isochrones. The color-magnitude diagrams show the presence of
differential extinction and possibly an age spread of a few megayears. We
convert the magnitudes into masses adopting both a single mean age of 3 Myr
isochrone and a constant star formation history from 2 to 4 Myr. We derive the
IMF after correcting for incompleteness due to crowding. The faintest stars
detected have a mass of 0.5 Msun and the data are more than 50% complete
outside a radius of 5 pc down to a mass limit of 1.1 Msun for 3 Myr old
objects. We find an IMF of dN/dlog(M) M^(-1.20+-0.2) over the mass range
1.1--20 Msun only slightly shallower than a Salpeter IMF. In particular, we
find no strong evidence for a flattening of the IMF down to 1.1 Msun at a
distance of 5 pc from the center, in contrast to a flattening at 2 Msun at a
radius of 2 pc, reported in a previous optical HST study. We examine several
possible reasons for the different results. If the IMF determined here applies
to the whole cluster, the cluster would be massive enough to remain bound and
evolve into a relatively low-mass globular cluster.
