RCW 38 is a deeply embedded young ( \sim 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 \sim 0.5 \times 0.5 pc ^ { 2 } obtained with NACO at the Very Large Telescope . Through comparison with evolutionary models we determine masses and extinction for \sim 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 \propto M ^ { - \alpha } , we derive the slope \alpha = 1.60 \pm 0.13 for the mass range 0.5 – 20 M _ { \sun } 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 \pm 0.11 for masses between 0.02 and 0.5 M _ { \sun } , or \alpha = 0.81 \pm 0.08 for masses between 0.02 and 1 M _ { \sun } . 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 M _ { \sun } ) .