We present new infrared, submillimeter, and millimeter observations of the dense core L673-7 and report the discovery of a low-luminosity, embedded Class 0 protostar driving a molecular outflow. L673-7 is seen in absorption against the mid-infrared background in 5.8, 8, and 24 micron Spitzer images, allowing for a derivation of the column density profile and total enclosed mass of L673-7, independent of dust temperature assumptions. Estimates of the core mass from these absorption profiles range from 0.2-4.5 solar masses. Millimeter continuum emission indicates a mass of about 2 solar masses, both from a direct calculation assuming isothermal dust and from dust radiative transfer models constrained by the millimeter observations. We use dust radiative transfer models to constrain the internal luminosity of L673-7, defined to be the luminosity of the central source and excluding the luminosity from external heating, to be 0.01-0.045 solar luminosities, with 0.04 solar luminosities the most likely value. L673-7 is thus classified as a very low luminosity object (VeLLO), and is among the lowest luminosity VeLLOs yet studied. We calculate the kinematic and dynamic properties of the molecular outflow in the standard manner, and we show that the expected accretion luminosity based on these outflow properties is greater than or equal to 0.36 solar luminosities. The discrepancy between this expected accretion luminosity and the internal luminosity derived from dust radiative transfer models indicates that the current accretion rate is much lower than the average rate over the lifetime of the outflow. Although the protostar embedded within L673-7 is consistent with currently being substellar, it is unlikely to remain as such given the substantial mass reservoir remaining in the core. ; Comment: 19 pages, 14 figures. Accepted by ApJ