  WASP-12b is a transiting hot Jupiter on a 1.09-day orbit around a late-F
star. Since the planet's discovery in 2008, the time interval between transits
has been decreasing by $29\pm 2$ msec year$^{-1}$. This is a possible sign of
orbital decay, although the previously available data left open the possibility
that the planet's orbit is slightly eccentric and is undergoing apsidal
precession. Here, we present new transit and occultation observations that
provide more decisive evidence for orbital decay, which is favored over apsidal
precession by a $\Delta\mathrm{BIC}$ of 22.3 or Bayes factor of 70,000. We also
present new radial-velocity data that rule out the R{\o}mer effect as the cause
of the period change. This makes WASP-12 the first planetary system for which
we can be confident that the orbit is decaying. The decay timescale for the
orbit is $P/\dot{P} = 3.25\pm 0.23$ Myr. Interpreting the decay as the result
of tidal dissipation, the modified stellar tidal quality factor is $Q'_\star =
1.8 \times10^{5}$.
