  We present an improved measurement of CP-violating asymmetries in B0 -> pi+
pi- decays based on a 78/fb 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 -> pi+ pi- CP eigenstate and identify the flavor of
the accompanying B meson from its decay products. From the asymmetry in the
distribution of the time intervals between the two B meson decay points, we
obtain the CP-violating asymmetry amplitudes Apipi =
+0.77+/-0.27(stat)+/-0.08(syst) and Spipi =
-1.23+/-0.41(stat)+0.08/-0.07(syst), where the statistical uncertainties are
determined from Monte Carlo pseudo-experiments. We rule out the CP-conserving
case, Apipi=Spipi=0, at the 99.93% confidence level. We discuss how these
results constrain the value of the CKM angle phi2.
