  We report a search for $B^{0}\to \eta \eta $ with a data sample corresponding
to an integrated luminosity of $698 \,{\rm fb}^{-1}$ containing $753 \times
10^{6}$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the
Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. The
branching fraction is measured to be $\mathcal{B}(B^{0} \to \eta \eta ) =
(7.6^{+2.7 +1.4}_{-2.3 -1.6}) \times 10^{-7}$ at the level of 3.3 standard
deviations above zero, which provides the first evidence for the decay $B^{0}
\to \eta \eta$.
