  We propose an analogue quantum simulator of a 1+1 D spacetime containing
non-causal curves,in particular, null geodesics going back in time, by means of
a dc-SQUID array embedded on an open superconducting transmission line. This is
achieved by mimicking the spatial dependence of the metric with the propagation
speed of the electromagnetic field in the simulator, which can be modulated by
an external magnetic flux. We show that it is possible to simulate a spacetime
region containing non-causal null geodesics, but not a full spacetime
containing a chronological horizon separating regions with non-causal null
geodesics and regions without them. This is in agreement with a recent
suggestion of analogue-gravity chronology protection mechanism by Barcel\'o et
al.
