  Chimera is a relatively new emerging phenomenon where coexistence of
synchronous and asynchronous state is observed in symmetrically coupled
dynamical units. We report observation of the chimera state in multiplex
networks where individual layer is represented by 1-d lattice with non-local
interactions. While, multiplexing does not change the type of the chimera state
and retains the multi-chimera state displayed by the isolated networks, it
changes the regions of the incoherence. We investigate emergence of
coherent-incoherent bifurcation upon varying the control parameters, namely,
the coupling strength and the network size. Additionally, we investigate the
effect of initial condition on the dynamics of the chimera state. Using a
measure based on the differences between the neighboring nodes which
distinguishes smooth and non-smooth spatial profile, we find the critical
coupling strength for the transition to the chimera state. Observing chimera in
a multiplex network with one to one inter layer coupling is important to gain
insight to many real world complex systems which inherently posses multilayer
architecture.
