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We present the first results from a new, deep (200ks) Chandra observation ofthe X-ray luminous galaxy cluster surrounding the powerful (L ~10^47 erg/s),high-redshift (z=1.067), compact-steep-spectrum radio-loud quasar 3C186. Thediffuse X-ray emission from the cluster has a roughly ellipsoidal shape andextends out to radii of at least ~60 arcsec (~500 kpc). The centroid of thediffuse X-ray emission is offset by 0.68(+/-0.11) arcsec (5.5+/-0.9 kpc) fromthe position of the quasar. We measure a cluster mass within the radius atwhich the mean enclosed density is 2500 times the critical density,r_2500=283(+18/-13)kpc, of 1.02 (+0.21/-0.14)x10^14 M_sun. The gas massfraction within this radius is f_gas=0.129(+0.015/-0.016). This value isconsistent with measurements at lower redshifts and implies minimal evolutionin the f_gas(z) relation for hot, massive clusters at 0<z<1.1. The measuredmetal abundance of 0.42(+0.08/-0.07) Solar is consistent with the abundanceobserved in other massive, high redshift clusters. The spatially-resolvedtemperature profile for the cluster shows a drop in temperature, from kT~8 keVto kT~3 keV, in its central regions that is characteristic of cooling coreclusters. This is the first spectroscopic identification of a cooling corecluster at z>1. We measure cooling times for the X-ray emitting gas at radii of50 kpc and 25 kpc of 1.7(+/-0.2)x10^9 years and 7.5(+/-2.6)x 10^8 years, aswell as a nominal cooling rate (in the absence of heating) of400(+/-190)M_sun/year within the central 100 kpc. In principle, the cooling gascan supply enough fuel to support the growth of the supermassive black hole andto power the luminous quasar. The radiative power of the quasar exceeds by afactor of 10 the kinematic power of the central radio source, suggesting thatradiative heating may be important at intermittent intervals in cluster cores.

High redshift X-ray cooling-core cluster associated with the luminous radio loud quasar 3C186