We have performed first-principles calculations to determine the surface atomic structure of a monolayer of Sb on the Si (111) surface. Scanning tunneling microscopy and low energy electron diffraction experiments have found (1X1), (2X1), and (root 3X root 3) reconstructions. Our calculations show that several structures have similar total energies, suggesting that different Sb geometries can coexist on Si (111). Besides the structures previously observed experimentally, we found a new structure (with similar total energy) formed by a sequence of two kind of trimers : one centered on a T-4 site and the following on a H-3 site.