  We demonstrate that the recent measurement of the cross section line shapes
of $e^+e^-\to \chi_{c0}\omega$ can be naturally explained by the molecular
picture for $Y(4260)$ where the $Y(4260)$ is treated as a hadronic molecule
dominated by $\bar{D}D_1(2420)+c.c.$ This result is consistent with properties
extracted for $Y(4260)$ as the $\bar{D}D_1(2420)+c.c.$ molecular state in other
reactions such as $e^+e^-\to J/\psi\pi\pi$, $h_c\pi\pi$, $\bar D D^*\pi +c.c.$,
and $\gamma X(3872)$.
