We present the discovery by the WASP-South survey of WASP-121 b, a new remarkable short-period transiting hot Jupiter. The planet has a mass of M_Jup, a radius of 1.865 ± 0.044 R_Jup, and transits every days an active F6-type main-sequence star (V = 10.4, M_⊙, 1.458 ± 0.030 R_⊙, T_eff = 6460 ± 140 K). A notable property of WASP-121 b is that its orbital semimajor axis is only ∼1.15 times larger than its Roche limit, which suggests that the planet is close to tidal disruption. Furthermore, its large size and extreme irradiation (∼7.1 10⁹ erg s⁻¹ cm⁻²) make it an excellent target for atmospheric studies via secondary eclipse observations. Using the TRAnsiting Planets and PlanetesImals Small Telescope, we indeed detect its emission in the z^′-band at better than ∼4σ, the measured occultation depth being 603 ± 130 ppm. Finally, from a measurement of the Rossiter–McLaughlin effect with the CORALIE spectrograph, we infer a sky-projected spin-orbit angle of . This result may suggest a significant misalignment between the spin axis of the host star and the orbital plane of the planet. If confirmed, this high misalignment would favour a migration of the planet involving strong dynamical events with a third body.