Context. The discovery of hundreds of quasi-stellar objects (QSOs) in the first gigayear of the Universe powered by already grown supermassive black holes (SMBHs) challenges our knowledge of SMBH formation. In particular, investigations of z > 6 QSOs that present notable properties can provide unique information on the physics of fast SMBH growth in the early Universe. Aims. We present the results of follow-up observations of the z = 6.515 radio-quiet QSO PSO167-13, which is interacting with a close companion galaxy. The PSO167-13 system has recently been proposed to host the first heavily obscured X-ray source at high redshift. The goals of these new observations are to confirm the existence of the X-ray source and to investigate the rest-frame UV properties of the QSO. Methods. We observed the PSO167-13 system with Chandra/ACIS-S (177 ks) and obtained new spectroscopic observations (7.2 h) with Magellan/FIRE. Results. No significant X-ray emission is detected from the PSO167-13 system, suggesting that the obscured X-ray source previously tentatively detected was either due to a strong background fluctuation or is highly variable. The upper limit (90% confidence level) on the X-ray emission of PSO167-13 ( L2−10 keV < 8.3 × 10 43 erg s −1) is the lowest available for a z > 6 QSO. The ratio between the X-ray and UV luminosity of αox < −1.95 makes PSO167-13 a strong outlier from the αox − LUV and LX − Lbol relations. In particular, its X-ray emission is more than six times weaker than the expectation based on its UV luminosity. The new Magellan/FIRE spectrum of PSO167-13 is strongly affected by unfavorable sky conditions, but the tentatively detected C IV and Mg II emission lines appear strongly blueshifted. Conclusions. The most plausible explanations for the X-ray weakness of PSO167-13 are intrinsic weakness or small-scale absorption by Compton-thick material. The possible strong blueshift of its emission lines hints at the presence of nuclear winds, which could be related to its X-ray weakness.