  We discuss the possibilities of producing the X(3872), which is assumed to be
a D \bar D^* bound state, in radiative decays of charmonia. We argue that the
ideal energy regions to observe the X(3872) associated with a photon in e^+e^-
annihilations are around the Y(4260) mass and around 4.45 GeV, due to the
presence of the S-wave D \bar D_1(2420) and D^* \bar D_1(2420) threshold,
respectively. Especially, if the Y(4260) is dominantly a D \bar D_1 molecule
and the X(3872) a D \bar D^* molecule, the radiative transition strength will
be quite large.
