We report the discovery of multi-scale X-ray jets from the accreting neutron star X-ray binary, Circinus X-1. The bipolar outflows show wide opening angles and are spatially coincident with the radio jets seen in new high-resolution radio images of the region. The morphology of the emission regions suggests that the jets from Circinus X-1 are running into a terminal shock with the interstellar medium, as is seen in powerful radio galaxies. This and other observations indicate that the jets have a wide opening angle, suggesting that the jets are either not very well collimated or precessing. We interpret the spectra from the shocks as cooled synchrotron emission and derive a cooling age of approximately 1600 yr. This allows us to constrain the jet power to be between 3e35 erg/s and 2e37 erg/s, making this one of a few microquasars with a direct measurement of its jet power and the only known microquasar that exhibits stationary large-scale X-ray emission.