We analyse the spectrum of perturbations of the de Sitter space on the one hand, while on the other hand we compute the location of the poles in the Conformal Field Theory (CFT) propagator at the border. The coincidence is striking, supporting a dS/CFT correspondence. We show that the spectrum of thermal excitations of the CFT at the past boundary I^- together with that spectrum at the future boundary I^+ is contained in the quasi-normal mode spectrum of the de Sitter space in the bulk.