  We report the first observation of a new charmonium state at a mass of
$(3.943 \pm 0.006 \pm 0.006) {GeV}/c^2$. This state, called X(3940), is
observed in the process $e^+ e^- \to J/\psi X(3940)$ in the spectrum of masses
recoiling against a reconstructed $J/\psi$. We also observe the decay of the
X(3940) into $D^* \bar{D}$ and measure the intrinsic width of this state to be
less than $52 MeV/c^2$ at the 90% C.L. These results are obtained from a $350
fb^{-1}$ data sample collected with the Belle detector near the $\Upsilon(4S)$
resonance, at the KEKB asymmetric energy $e^+ e^-$ collider.
