\noindent ``Integrability meeting ENS/IPhT'' \\ \\ We demonstrate by explicit multi-loop calculation that gamma-deformed planar N = 4 SYM, supplemented with a set of double-trace counter-terms, has two nontrivial fixed points in the recently proposed double scaling limit, combining vanishing ’t Hooft coupling and large imaginary deformation parameter. We provide evidence that, at the fixed points, the theory is described by an integrable non-unitary four-dimensional CFT. We find a closed expression for the four-point correlation function of the simplest protected operators and use it to compute the exact conformal data of operators with arbitrary Lorentz spin. We conjecture that both conformal symmetry and integrability should survive in gamma-deformed planar N = 4 SYM for arbitrary values of the deformation parameters. \\ \\ (IPhT organizers: Ivan Kostov and Didina Serban)