This report describes an observation of mixing-induced CP violation and a measurement of the CP violation parameter, sin(2phi_1), with the Belle detector at the KEKB asymmetric e+e- collider. Using a data sample of 29.1 fb-1 recorded on the Upsilon(4S) resonance that contains 31.3 million BBbar pairs, we reconstruct decays of neutral B mesons to the following CP eigenstates: J/psi K_S^0, psi(2S) K_S^0, chi_c1 K_S^0, eta_c K_S^0, J/psi K_L^0 and J/psi K^*0. The flavor of the accompanying B meson is identified by combining information from primary and secondary leptons, K+/- mesons, lambda baryons, slow and fast pions. The proper-time interval between the two B meson decays is determined from the distance between the two decay vertices measured with a silicon vertex detector. The result sin(2phi_1) = 0.99 +/- 0.14(stat) +/- 0.06(syst) is obtained by applying a maximum likelihood fit to the 1137 candidate events. We conclude that there is large CP violation in the neutral B meson system. A zero value for sin(2phi_1) is ruled out by more than six standard deviations.