  If the recently-discovered charmonium-like state X(3872) is a loosely-bound
S-wave molecule of the charm mesons D^0 \bar D^{*0} or D^{*0} \bar D^0, it can
be produced through the weak decay of the B meson into D^0 \bar D^{*0} K or
D^{*0} \bar D^0 K followed by the coalescence of the charm mesons at a
long-distance scale set by the scattering length of the charm mesons. The
long-distance factors in the amplitude for the decay B \to XK are determined by
the binding energy of X, while the short-distance factors are essentially
determined by the amplitudes for B \to D^0 \bar D^{*0} K and B \to D^{*0} \bar
D^0 K near the thresholds for the charm mesons. We obtain a crude determination
of the short-distance amplitudes by analyzing data from the Babar collaboration
on the branching fractions for B\to \bar D^{(*)} D^{(*)} K using a
factorization assumption, heavy quark symmetry, and isospin symmetry. The
resulting order-of-magnitude estimate of the branching fraction for B^+ \to X
K^+ is compatible with observations provided that J/\psi \pi^+ \pi^- is a major
decay mode of the X. The branching fraction for B^0 \to X K^0 is predicted to
be suppressed by more than an order of magnitude compared to that for B^+ \to X
K^+.
