In this note we study constant mean curvature surfaces in asymptotically flat
3-manifolds. We prove that, in an asymptotically flat 3-manifold with positive
mass, stable spheres of given constant mean curvature outside a fixed compact
subset are unique. Therefore we are able to conclude that there is a unique
foliation of stable spheres of constant mean curvature in an asymptotically
flat 3-manifold with positive mass.Comment: 22 page