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We propose deep Chandra ACIS observations and joint HST narrow band imaging of the nearby Compton-thick AGN ESO137-G034. The recent Chandra discovery of extended kpc-scale hard X-ray continuum (3-6 keV) and Fe Ka emission in Compton-thick AGN provides physical constraints on the obscuring torus and demonstrates the impact of the supermassive black hole (SMBH) on the host galaxy via feedback. Comparing deep Chandra data with multi-wavelength high resolution data (e.g. HST comma ALMA comma VLT-SINFONI) comma we will conduct an unprecedented comprehensive analysis of the extended X-ray emission comma and the multi-phase interstellar media (i.e. cold and warm molecular gas comma ionized gas comma and dust) at sub-arcsec resolution to ultimately understand how the central SMBH interacts with and impacts the host galaxy.