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 $1.183_{-0.062}^{+0.064}$ M Jup, a radius of 1.865 ± 0.044 R Jup, and transits every $1.274\,9255_{-0.000\,0025}^{+0.000\,0020}$ days an active F6-type main-sequence star (V = 10.4, $1.353_{-0.079}^{+0.080}$ 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 $257{^{\circ}_{.}} 8_{-5{^{\circ}_{.}} 5}^{+5{^{\circ}_{.}} 3}$ . 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.