We present the results of an amplitude analysis of B-0 --> J/psi K- pi(+) decays. A new charged charmoniumlike state Z(c)(4200)(+) decaying to J/psi pi(+) is observed with a significance of 6.2 sigma. The mass and width of the Z(c)(4200)(+) are 4196(-29-13)(+31+17) MeV/c(2) and 370(-70-132)(+70+70) MeV, respectively; the preferred assignment of the quantum numbers is J(P) = 1(+). In addition, we find evidence for Z(c)(4430)(+) --> J/psi pi(+). The analysis is based on a 711 fb(-1) data sample collected by the Belle detector at the asymmetric-energy e(+)e(-) collider KEKB.