  We present the discovery by the WASP-South survey, in close collaboration
with the Euler and TRAPPIST telescopes, of WASP-121 b, a new remarkable
short-period transiting hot Jupiter, whose planetary nature has been
statistically validated by the PASTIS software. The planet has a mass of
$1.183_{-0.062}^{+0.064}$ $M_{\mathrm{Jup}}$, a radius of 1.865 $\pm$ 0.044
$R_{\mathrm{Jup}}$, and transits every $1.2749255_{-0.0000025}^{+0.0000020}$
days an active F6-type main-sequence star ($V$=10.4, $1.353_{-0.079}^{+0.080}$
$M_{\odot}$, 1.458 $\pm$ 0.030 $R_{\odot}$, $T_{\mathrm{eff}}$ = 6460 $\pm$ 140
K). A notable property of WASP-121 b is that its orbital semi-major axis is
only $\sim$1.15 times larger than its Roche limit, which suggests that the
planet might be close to tidal disruption. Furthermore, its large size and
extreme irradiation ($\sim$$7.1\:10^{9}$ erg $\mathrm{s}^{-1}
\mathrm{cm}^{-2}$) make it an excellent target for atmospheric studies via
secondary eclipse observations. Using the TRAPPIST telescope, we indeed detect
its emission in the $z'$-band at better than $\sim$4$\sigma$, the measured
occultation depth being 603 $\pm$ 130 ppm. Finally, from a measurement of the
Rossiter-McLaughlin effect with the CORALIE spectrograph, we infer a
sky-projected spin-orbit angle of $257.8_{-5.5}^{+5.3}$ deg. This result
indicates a significant misalignment between the spin axis of the host star and
the orbital plane of the planet, the planet being in a nearly polar orbit. Such
a high misalignment suggests a migration of the planet involving strong
dynamical events with a third body.
