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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 O(x) O(0), then the large spin ℓ Fock space states [TT ... T]_ℓ also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an 〈OOOO〉doi:10.1007/jhep09(2015)019 fatcat:aeglplv6ozcv5jg6dcobxaoesu