We report the discovery of an active galactic nucleus (AGN) pair in the interacting galaxy system IRAS 20210+1121 at z = 0.056. An XMM-Newton observation reveals the presence of an obscured (N(H) similar to 5 x 10(23) cm(-2)), Seyfert-like (L(2)-10 keV = 4.7 x 10(42) erg s(-1)) nucleus in the northern galaxy, which lacks unambiguous optical AGN signatures. Our spectral analysis also provides strong evidence that the IR-luminous southern galaxy hosts a Type 2 quasar embedded in a bright starburst emission. In particular, the X-ray primary continuum from the nucleus appears totally depressed in the XMM-Newton band as expected in the case of a Compton-thick absorber, and only the emission produced by Compton scattering ("reflection") of the continuum from circumnuclear matter is seen. As such, IRAS 20210+1121 seems to provide an excellent opportunity to witness a key, early phase in the quasar evolution predicted by the theoretical models of quasar activation by galaxy collisions.