While theoretical arguments predict that most of the early growth of supermassive black holes (SMBHs) happened during heavily obscured phases of accretion, current methods used for selecting z > 6 quasars (QSOs) are strongly biased against obscured QSOs, thus considerably limiting our understanding of accreting SMBHs during the first gigayear of the Universe from an observational point of view. We report the Chandra discovery of the first heavily obscured QSO candidate in the early universe, hosted by a close (≈5 kpc) galaxy pair at z = 6.515. One of the members is an optically classified type-1 QSO, PSO167–13. The companion galaxy was first detected as a [C II] emitter by Atacama large millimeter array (ALMA). An X-ray source is significantly (P = 0.9996) detected by Chandra in the 2–5 keV band, with < 1.14 net counts in the 0.5–2 keV band, although the current positional uncertainty does not allow a conclusive association with either PSO167–13 or its companion galaxy. From X-ray photometry and hardness-ratio arguments, we estimated an obscuring column density of N_H > 2 × 10²⁴ cm⁻² and N_H > 6 × 10²³ cm⁻² at 68% and 90% confidence levels, respectively. Thus, regardless of which of the two galaxies is associated with the X-ray emission, this source is the first heavily obscured QSO candidate at z > 6.