  We consider the initial-value problem for the one-dimensional nonlinear
Schr\"odinger equation in the presence of an attractive delta potential. We
show that for sufficiently small initial data, the corresponding global
solution decomposes into a small solitary wave plus a radiation term that
decays and scatters as $t\to\infty$. In particular, we establish the asymptotic
stability of the family of small solitary waves.
