We present Multi-Unit Spectroscopic Explorer (MUSE) integral-field spectroscopy of ESO 253$-$G003, which hosts a known Active Galactic Nucleus (AGN) and the periodic nuclear transient ASASSN-14ko, observed as part of the All-weather MUse Supernova Integral-field of Nearby Galaxies (AMUSING) survey. The MUSE observations reveal that the inner region hosts two AGN separated by $1.4pm0.1~rm{kpc}$ ($approx 1.!!^{primeprime}7$). The brighter nucleus has asymmetric broad, permitted emission-line profiles and is associated with the archival AGN designation. The fainter nucleus does not have a broad emission-line component but exhibits other AGN characteristics, including $v_{rm{FWHM}}approx 700~rm{km}~rm{s}^{-1}$ forbidden line emission, $log_{10}(rm{[OIII]}/rm{H}beta) approx 1.1$, and high excitation potential emission lines such as [Fe$~$VII]$~lambda6086$ and He$~$II$~lambda4686$. The host galaxy exhibits a disturbed morphology with large kpc-scale tidal features, potential outflows from both nuclei, and a likely superbubble. A circular relativistic disk model cannot reproduce the asymmetric broad emission-line profiles in the brighter nucleus, but two non-axisymmetric disk models provide good fits to the broad emission-line profiles: an elliptical disk model and a circular disk + spiral arm model. Implications for the periodic nuclear transient ASASSN-14ko are discussed.
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