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A potentially powerful approach to study early galaxy formation is through massive relic galaxies (MRGs) which are local analogs of the high-redshift d_commared nuggetsd_comma thought to represent progenitors of today.s early-type galaxies. When a luminous hot halo is present comma X-ray observations of the diffuse hot gas of MRGs provide the most viable means to measure the gravitating mass profile comma and X-rays afford a powerful direct approach to study cooling and AGN feedback. Here we propose a joint Chandra -HST observation of NGC 5872 comma a very massive MRG comma to map its inner mass profile (<virgulR_e) comma especially by measuring the stellar mass-to-light ratio comma and to examine the magnitude of AGN feedback through image analysis and the radial profile of the ratio of the cooling and free-fall times.