We propose and demonstrate that a γγ collider with Wyy ≤ 12 GeV can be added to the European XFEL with a minimal disruption to its main program. High-energy photons will be obtained by Compton scattering of 0.5 μm laser photons on the existing 17.5 GeV electron beams. Such a γγ collider would be an excellent place for the development and application of modern technologies: powerful lasers, optical cavities, superconducting linacs, and low-emittance electron sources — as well as training the next generation of accelerator physicists and engineers. The physics program would include spectroscopy of C = + resonances in various JP states (bb, ¯ cc¯, four-quark states, quark molecules and other exotica) in a mass range barely scratched by past and not covered by any current or planned experiments. Variable circular and linear polarizations will help in the determination of quantum numbers and measurement of polarization components of the γγ cross section (σ, σk, σ0, σ2).