  We present a dispersion relation in conformal field theory which expresses
the four point function as an integral over its single discontinuity.
Exploiting the analytic properties of the OPE and crossing symmetry of the
correlator, we show that in perturbative settings the correlator depends only
on the spectrum of the theory, as well as the OPE coefficients of certain low
twist operators, and can be reconstructed unambiguously. In contrast to the
Lorentzian inversion formula, the validity of the dispersion relation does not
assume Regge behavior and is not restricted to the exchange of spinning
operators. As an application, the correlator $\langle \phi \phi \phi \phi
\rangle$ in $\phi^4$ theory at the Wilson-Fisher fixed point is computed in
closed form to order $\epsilon^2$ in the $\epsilon$ expansion.
