Detailed knowledge of the initial distribution of stellar masses at birth (known as the initial mass function or IMF) is necessary to predict and understand the evolution of stellar systems, such as clusters and galaxies. Unfortunately, stellar evolution theory cannot predict the form of this critical function and the origin of the stellar IMF remains one of the major unsolved problems of modern astrophysics.Stars form in the cold dense cores of interstellar molecular clouds and the detailed knowledge of the spectrum of masses of such cores is clearly a key for the understanding of the origin of the IMF. To date, observations have presented somewhat contradictory evidence relating to this issue. Here we present a new and more robust determination of the dense core mass function. We find the core mass function to be surprisingly similar to the stellar IMF, modified by a uniform star formation efficiency of about 30%. This suggests that the distribution of stellar birth masses is a direct product of the fragmentation/coalescence process in a molecular cloud.