  RCW 38 is a deeply embedded young (~1 Myr), massive star cluster located at a
distance of 1.7 kpc. Twice as dense as the Orion Nebula Cluster, orders of
magnitude denser than other nearby star forming regions, and rich in massive
stars, RCW 38 is an ideal place to look for potential differences in brown
dwarf formation efficiency as a function of environment. We present deep, high
resolution adaptive optics data of the central ~0.5x0.5 pc^2 obtained with NACO
at the Very Large Telescope. Through comparison with evolutionary models we
determine masses and extinction for ~480 candidate members, and derive the
first Initial Mass Function (IMF) of the cluster extending into the substellar
regime. Representing the IMF as a set of power laws in the form
dN/dM~M^(-alpha), we derive the slope alpha = 1.60+-0.13 for the mass range 0.5
- 20 MSun which is shallower than the Salpeter slope, but in agreement with
results in several other young massive clusters. At the low-mass side, we find
alpha = 0.71+-0.11 for masses between 0.02 and 0.5 MSun, or alpha = 0.81+-0.08
for masses between 0.02 and 1 MSun. Our result is in agreement with the values
found in other young star-forming regions, revealing no evidence that a
combination of high stellar densities and the presence of numerous massive
stars affect the formation efficiency of brown dwarfs and very-low mass stars.
We estimate that the Milky Way galaxy contains between 25 and 100 billion brown
dwarfs (with masses > 0.03 MSun).
