  It is known that ground states of the pseudo-relativistic Boson stars exist
if and only if the stellar mass $N>0$ satisfies $N<N^*$, where the finite
constant $N^*$ is called the critical stellar mass. Lieb and Yau conjecture in
[Comm. Math. Phys., 1987] that ground states of the pseudo-relativistic Boson
stars are unique for each $N<N^*$. In this paper, we prove that the above
uniqueness conjecture holds for the particular case where $N>0$ is small
enough.
