We present the results of the analysis of two Chandra observations of Circinus X-1 performed in 2007, for a total exposure time of ~50 ks. The source was observed with the High Resolution Camera during a long X-ray low-flux state of the source. Cir X-1 is an accreting neutron-star binary system that exhibits ultra-relativistic arcsec-scale radio jets and an extended arcmin-scale radio nebula. Furthermore, a recent paper has shown an X-ray excess on arcmin-scale prominent on the side of the receding radio jet. In our images we clearly detect X-ray structures both on the side of the receding and the approaching radio jet. The X-ray emission is consistent with being from synchrotron origin. Our detection is consistent with neutron-star binaries being as efficient as black-hole binaries in producing X-ray outflows, despite their shallower gravitational potential.