We analyze new Chandra observations of the nearest (D = 4 Mpc) Seyfert 2 active galaxy, Circinus, and match them to pre-existing radio, infrared, and optical data to study the kpc-scale emission. The proximity of Circinus allows us to observe in striking detail the structure of the radio lobes, revealing for the first time edge-brightened emission in both X-rays and radio. After considering various other possible scenarios, we show that this extended emission in Circinus is most likely caused by a jet-driven outflow, which is driving shells of strongly shocked gas into the halo of the host galaxy. In this context, we estimate Mach numbers M{approx}2.7-3.6 and M{approx}2.8-5.3 for the W and E shells, respectively. We derive temperatures of 0.74{sup +0.06} {sub -0.05} keV and 0.8-1.8 keV for the W and E shells and an expansion velocity of {approx}900-950 km s{sup -1}. We estimate that the total energy (thermal and kinetic) involved in creating both shells is {approx}2 Multiplication-Sign 10{sup 55} erg, and their age is {approx}10{sup 6} yr. Comparing these results with those we previously obtained for Centaurus A, NGC 3801, and Mrk 6, we show that these parameters scale approximately with the radio power of the parent active galactic nucleus (AGN). The spatial coincidence between the X-ray and edge-brightened radio emission in Circinus resembles the morphology of some supernova remnant shocks. This parallel has been expected for AGNs but has never been observed before. We investigate what underlying mechanisms both types of systems may have in common, arguing that, in Circinus, the edge-brightening in the shells may be accounted for by a B field enhancement caused by shock compression but do not preclude some local particle acceleration. These results can be extrapolated to other low-power systems, particularly those with late-type hosts.