We present ALMA observations of the inner 1 (1.2 kpc) of the Circinus galaxy, the nearest Seyfert. We target CO (1-0) in the region associated with a well-known multiphase outflow driven by the central active galactic nucleus (AGN). While the geometry of Circinus and its outflow make disentangling the latter difficult, we see indications of outflowing molecular gas at velocities consistent with the ionized outflow. We constrain the mass of the outflowing molecular gas to be 1.5e5 -5.1e6 solar masses, yielding a molecular outflow rate of 0.35-12.3 solar masses per year. The values within this range are comparable to the star formation rate in Circinus, indicating that the outflow indeed regulates star formation to some degree. The molecular outflow in Circinus is considerably lower in mass and energetics than previously-studied AGN-driven outflows, especially given its high ratio of AGN luminosity to bolometric luminosity. The molecular outflow in Circinus is, however, consistent with some trends put forth in Cicone et al. (2014), including a linear relation between kinetic power and AGN luminosity, as well as its momentum rate vs. bolometric luminosity (although the latter places Circinus among the starburst galaxies in that sample). We detect additional molecular species including CN and C17O.