We report on 5 Chandra observations of the X-ray afterglow of the Gamma-Ray Burst GRB 060729 performed between 2007 March and 2008 May . In all five observations the afterglow is clearly detected . The last Chandra pointing was performed on 2008-May-04 , 642 days after the burst - the latest detection of a GRB X-ray afterglow ever . A reanalysis of the Swift XRT light curve together with the three detections by Chandra in 2007 reveals a break at \sim 1.0 Ms after the burst with a slight steepening of the decay slope from \alpha = 1.32 to 1.61 . This break coincides with a significant hardening of the X-ray spectrum , consistent with a cooling break in the wind medium scenario , in which the cooling frequency of the afterglow crosses the X-ray band . The last two Chandra observations in 2007 December and 2008 May provide evidence for another break at about one year after the burst . If interpreted as a jet break , this late-time break implies a jet half opening angle of \sim 14 ^ { \circ } for a wind medium . Alternatively , this final break may have a spectral origin , in which case no jet break has been observed and the half-opening angle of the jet of GRB 060729 must be larger than \sim 15 ^ { \circ } for a wind medium . We compare the X-ray afterglow of GRB 060729 in a wind environment with other bright X-ray afterglows , in particular GRBs 061121 and 080319B , and discuss why the X-ray afterglow of GRB 060729 is such an exceptionally long-lasting event .