  We have studied the low-lying excitations of a chain of coupled circuit-QED
systems, and report several intriguing properties of its two nearly degenerate
ground states. The ground states are Schr\"odinger cat states at a truly large
scale, involving maximal entanglement between the resonator and the qubit, and
are mathematically equivalent to Majorana bound states. With a suitable design
of physical qubits, they are protected against local fluctuations and
constitute a non-local qubit. Further, they can be probed and manipulated
coherently by attaching an empty resonator to one end of the circuit-QED chain.
