Aims. Using the deepest (370 ks) Chandra observation of a high-redshift galaxy cluster, we perform a detailed characterization of the intra-cluster medium (ICM) of WARPJ1415.1+3612 at z = 1.03, particularly its core region. We also explore the connection between the ICM core properties and the radio/optical properties of the brightest cluster galaxy (BCG). Methods. We perform a spatially resolved analysis of the ICM to obtain temperature, metallicity and surface brightness profiles over the 8-400 kpc radial range. We measure the following cool-core diagnostics: central temperature drop, central metallicity excess, central cooling time, and central entropy. Using the deprojected temperature and density profiles, we accurately derive the cluster hydrostatic mass at different overdensities. In addition to the X-ray data, we use archival radio VLA imaging and optical GMOS spectroscopy of the central galaxy to investigate the feedback between the central galaxy and the ICM. Results. Our spatially resolved spectral analysis shows a significant temperature drop from a maximum of 8.0 keV to a projected core value T c = 4.6 ± 0.4 keV, and a remarkably high central iron abundance peak, Z Fe,c = 3.60 +1.50 −0.85 Z , measured within a radius of 12 kpc. We measure M 500 = M(r < R 500 ) = 2.4 ± 0.4 M and a corresponding gas fraction f gas = 0.10 ± 0.02. The central cooling time is shorter than 0.1 Gyr and the entropy K c is equal to 9.9 keV cm 2 . We detect a strong [OII] emission line in the optical spectra of the BCG with an equivalent width of -25 Å, for which we derive a star formation rate within the range 2-8 M yr −1 . The VLA data reveals a central radio source coincident with the BCG with a luminosity L 1.4 GHz = 2.0 × 10 25 W Hz −1 , and a faint one-sided jet-like feature with an extent of ∼80 kpc. We do not find clear evidence for cavities associated to the radio AGN activity. Conclusions. Our analysis shows that WARPJ1415 has a well developed cool-core with ICM properties similar to those found in the local Universe. Its properties and the clear sign of feedback activity found in the central galaxy in the optical and radio bands, show that feedback processes are already established at z ∼ 1 (a lookback time of 7.8 Gyr). In addition, the presence of a strong metallicity peak shows that the central regions have been promptly enriched by star formation processes in the central galaxy already at z > 1. Our results significantly constrain the timescale for the formation and self-stabilization of cool-cores.