We report on the analysis of a deep Chandra observation of the high-magnetic field pulsar (PSR) J1119-6127 and its compact pulsar wind nebula (PWN) taken in October 2019, three years after the source went into outburst. The 0.5-7 keV post-outburst (2019) spectrum of the pulsar is best described by a two-component blackbody plus powerlaw model with a temperature of 0.2±0.1 keV, photon index Γ=1.8±0.4 and X-ray luminosity of 1.9 +0.3 −0.3 ×10 33 erg s −1 , consistent with its pre-burst quiescent phase. We find that the pulsar has gone back to quiescence. The compact nebula shows a jet-like morphology elongated in the north-south direction, similar to the pre-burst phase. The postoutburst PWN spectrum is best fit by an absorbed powerlaw with a photon index Γ=2.3±0.5 and a flux of 3.2 +0.3 −0.2 ×10 −14 erg cm −2 s −1 (0.5-7 keV). The PWN spectrum shows evidence of spectral softening in the post-outburst phase, with the pre-burst photon index Γ=1.2±0.4 changing to Γ=2.3±0.5 and pre-burst luminosity of 1.5 +0.5 −0.4 ×10 32 erg s −1 changing to 2.7 +0.3 −0.2 ×10 32 erg s −1 in the 0.5-7 keV band, suggesting magnetar outbursts can impact PWNe. The observed timescale for returning to quiescence, of just a few years, implies a rather fast cooling process, and favors a scenario where J1119 is temporarily powered by magnetic energy following the magnetar outburst, in addition to its spin-down energy.