  We investigate the possibility of obtaining chimera state solutions of the
non-local Complex Ginzburg-Landau Equation (NLCGLE) in the strong coupling
limit when it is important to retain amplitude variations. Our numerical
studies reveal the existence of a variety of amplitude mediated chimera states
(including stationary and non-stationary two cluster chimera states), that
display intermittent emergence and decay of amplitude dips in their phase
incoherent regions. The existence regions of the single-cluster chimera state
and both types of two cluster chimera states are mapped numerically in the
parameter space of $C_1$ and $C_2$ the linear and nonlinear dispersion
coefficients respectively of the NLCGLE. They represent a new domain of
dynamical behaviour in the well explored rich phase diagram of this system. The
amplitude mediated chimera states may find useful applications in understanding
spatio-temporal patterns found in fluid flow experiments and other strongly
coupled systems.
