In this letter we signalize the possibility of applying a quantum chaos as an element of high sensitivity which serves to detect small changes in length generated by gravitational waves. We propose the construction of a double-bar antenna with a coupling Josephson junction in its center-of-mass. In fact the new antenna is a single Josephson junction with massive bulk contacts, like a single-junction SQUID but with free ends. Computer experiments demonstrate that very small changes generated by the variation of the distance between the bulk plates of the junction capacitance will produce a variety of very different intermittency routes to chaos. A concrete numerical example illustrates the smallness of a quantum of chaos and thus the extraordinary sensitivity of the proposed method.