Observation of the Decay $B^{0} \to \pi^{0}\pi^{0}$

We present an observation of the decay $B^{0} \to \pi^{0} \pi^{0}$ based on a sample of 124 million $B\bar{B}$ pairs recorded by the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We observe $46 \pm 13 \pm 3$ events, where the first error is statistical and the second is systematic, corresponding to a significance of 4.2 standard deviations including systematic uncertainties. We measure the branching fraction $\BR(B^{0} \to \pi^{0} \pi^{0}) = (2.1 \pm 0.6 \pm 0.3) \times 10^{-6}$, averaged over $B^{0}$ and $\bar{B}^{0}$ decays.