  Measurements of stellar velocities and variable X-ray emission near the
centre of the Milky Way have provided the strongest evidence so far that the
dark mass concentrations seen in many galactic nuclei are likely supermassive
black holes, but have not yet excluded several alternative configurations. Here
we report ten years of high resolution astrometric imaging that allow us to
trace two thirds of the orbit of the star currently closest to the compact
radio source and massive black hole candidate SgrA*. In particular, we have
observed both peri- and apocentre passages. Our observations show that the star
is on a bound, highly elliptical Keplerian orbit around SgrA*, with an orbital
period of 15.2 years and a peri-centre distance of only 17 light hours. The
orbital elements require an enclosed point mass of 3.7+-1.5x10^6 solar masses.
The data exclude with high confidence that the central dark mass consists of a
cluster of astrophysical objects or massive, degenerate fermions, and strongly
constrain the central density structure.
