We report the observation of the decay B0-->pi(0)pi(0), using a 253 fb(-1) data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB e(+)e(-) collider. The measured branching fraction is B(B0-->pi(0)pi(0))=(2.3(+0.4+0.2)(-0.5-0.3))x10(-6), with a significance of 5.8 standard deviations including systematic uncertainties. We also make a measurement of the direct CP violating asymmetry in this mode.