Chimera states, representing a spontaneous breakup of a population of identical oscillators that are identically coupled, into subpopulations displaying synchronized and desynchronized behavior, have traditionally been found to exist in weakly coupled systems and with some form of nonlocal coupling between the oscillators. Here we show that neither the weak-coupling approximation nor nonlocal coupling are essential conditions for their existence. We obtain, for the first time, amplitude-mediated chimera states in a system of globally coupled complex Ginzburg-Landau oscillators. We delineate the dynamical origins for the formation of such states from a bifurcation analysis of a reduced model equation and also discuss the practical implications of our discovery of this broader class of chimera states.