  We prove a chain rule for the Goodwillie calculus of functors from spectra to
spectra. We show that the (higher) derivatives of a composite functor $FG$ at a
base object $X$ are given by taking the composition product (in the sense of
symmetric sequences) of the derivatives of $F$ at $G(X)$ with the derivatives
of $G$ at $X$. We also consider the question of finding $P_n(FG)$, and give an
explicit formula for this when $F$ is homogeneous.
