As part of our ongoing NTT SoFI survey for variability in young free-floating planets and low-mass brown dwarfs, we detect significant variability in the young, free-floating planetary-mass object PSO J318.5-22, likely due to rotational modulation of inhomogeneous cloud cover. A member of the 23 +/- 3 Myr beta Pic moving group, PSO J318.5-22 has T-eff = 1160(-40)(+30) K and a mass estimate of 8.3 +/- 0.5 M-Jup for a 23 +/- 3 Myr age. PSO J318.5-22 is intermediate in mass between 51 Eri b and beta Pic b, the two known exoplanet companions in the beta Pic moving group. With variability amplitudes from 7% to 10% in J(S) at two separate epochs over 3-5 hr observations, we constrain the rotational period of this object to >5 hr. In K-S, we marginally detect a variability trend of up to 3% over a 3 hr observation. This is the first detection of weather on an extrasolar planetary-mass object. Among L dwarfs surveyed at high photometric precision (