  Scattering of radial $H^1$ solutions to the 3D focusing cubic nonlinear
Schr\"odinger equation below a mass-energy threshold $M[u]E[u] < M[Q]E[Q]$ and
satisfying an initial mass-gradient bound $\|u_0\|_{L^2} \|\nabla u_0 \|_{L^2}
< \|Q\|_{L^2} \|\nabla Q\|_{L^2}$, where $Q$ is the ground state, was
established in Holmer-Roudenko (2007). In this note, we extend the result in
Holmer-Roudenko (2007) to non-radial $H^1$ data. For this, we prove a
non-radial profile decomposition involving a spatial translation parameter.
Then, in the spirit of Kenig-Merle (2006), we control via momentum conservation
the rate of divergence of the spatial translation parameter and by a convexity
argument based on a local virial identity deduce scattering. An application to
the defocusing case is also mentioned.
