  We have used QCD sum rules to study the newly observed charged state
$Z_c(4025)$ as a hidden-charm $D^*\bar D^*$ molecular state with the quantum
numbers $I^G(J^{P})=1^+(1^{+})$. Using a $D^*\bar D^*$ molecular interpolating
current, we have calculated the two-point correlation function and the spectral
density up to dimension eight at leading order in $\alpha_s$. The extracted
mass is $m_X=(4.04\pm0.24)$ GeV. This result is compatible with the observed
mass of $Z_c(4025)$ within the errors, which implies a possible molecule
interpretation of this new resonance. We also predict the mass of the
corresponding hidden-bottom $B^*\bar B^*$ molecular state:
$m_{Z_b}=(9.98\pm0.21)$ GeV.
