  Classical field configurations such as the Coulomb potential and
Schwarzschild solution are built from the t-channel exchange of many light
degrees of freedom. We study the CFT analog of this phenomenon, which we term
the `eikonalization' of conformal blocks. We show that when an operator $T$
appears in the OPE $\mathcal{O}(x) \mathcal{O}(0)$, then the large spin $\ell$
Fock space states $[TT \cdots T]_{\ell}$ also appear in this OPE with a
computable coefficient. The sum over the exchange of these Fock space states in
an $\langle \mathcal{O} \mathcal{O} \mathcal{O} \mathcal{O} \rangle$ correlator
build the classical `$T$ field' in the dual AdS description. In some limits the
sum of all Fock space exchanges can be represented as the exponential of a
single $T$ exchange in the 4-pt correlator of $\mathcal{O}$. Our results should
be useful for systematizing $1/\ell$ perturbation theory in general CFTs and
simplifying the computation of large spin OPE coefficients. As examples we
obtain the leading $\log \ell$ dependence of Fock space conformal block
coefficients, and we directly compute the OPE coefficients of the simplest
`triple-trace' operators.
