Dual active galactic nuclei (AGNs) and offset AGNs are kpc-scale separation supermassive black holes pairs created during galaxy mergers, where both or one of the black holes are AGNs, respectively. These dual and offset AGNs are valuable probes of the link between mergers and AGNs but are challenging to identify. Here we present Chandra/ACIS observations of 12 optically selected dual AGN candidates at z < 0.34, where we use the X-rays to identify AGNs. We also present Hubble Space Telescope/Wide Field Camera 3 observations of 10 of these candidates, which reveal any stellar bulges accompanying the AGNs. We discover a dual AGN system with separation δx = 2.2 kpc, where the two stellar bulges have coincident [O iii] λ5007 and X-ray sources. This system is an extremely minor merger (460:1) that may include a dwarf galaxy hosting an intermediate mass black hole. We also find six single AGNs, and five systems that are either dual or offset AGNs with separations δx < 10 kpc. Four of the six dual AGNs and dual/offset AGNs are in ongoing major mergers, and these AGNs are 10 times more luminous, on average, than the single AGNs in our sample. This hints that major mergers may preferentially trigger higher luminosity AGNs. Further, we find that confirmed dual AGNs have hard X-ray luminosities that are half of those of single AGNs at fixed [O iii] λ5007 luminosity, on average. This could be explained by high densities of gas funneled to galaxy centers during mergers, and emphasizes the need for deeper X-ray observations of dual AGN candidates.