We present an improved measurement of CP-violating asymmetries in B 0→π+π- decays based on a 78 fb -1 data sample collected at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+ e- collider. We reconstruct one neutral B meson as a B0→π+π - CP eigenstate and identify the flavor of the accompanying B meson from inclusive properties of its decay products. We apply an unbinned maximum likelihood fit to the distribution of the time intervals between the two B meson decay points. The fit yields the CP-violating asymmetry amplitudes A ππ= +0.77 ±0.27(stat) ±0.08(syst) and S ππ=-1.23 ±0.41(stat) -0.07 +0.08(syst), where the statistical uncertainties are determined from the Monte Carlo pseudoexperiments. We obtain confidence intervals for CP-violating asymmetry parameters Aππ and Sππ based on a frequentist approach. We rule out the CP-conserving case, A ππ=Sππ=0, at the 99.93% confidence level. We discuss how these results constrain the value of the Cabibbo-Kobayashi-Maskawa (CKM) angle φ2. © 2003 The American Physical Society.