  We report a measurement of the decay B0 --> rho0 pi0, using 386 x 10^6 BB-bar
pairs collected at the Upsilon(4S) resonance with the Belle detector at the
KEKB asymmetric-energy e+e- collider. We detect 51^{+14}_{-13} signal events
with a significance of 4.2 standard deviations, including systematic
uncertainties, and measure the branching fraction to be B(B0 --> rho0 pi0) =
(3.12^{+0.88}_{-0.82} (stat) +/- 0.33 (syst) ^{+0.50}_{-0.68} (model)) x
10^{-6}. We also perform the first measurement of direct CP violating asymmetry
in this mode.
