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We present ALMA observations of the [CII] fine structure line and theunderlying far-infrared (FIR) dust continuum emission in J1120+0641, the mostdistant quasar currently known (z=7.1). We also present observations targetingthe CO(2-1), CO(7-6) and [CI] 369 micron lines in the same source obtained atthe VLA and PdBI. We find a [CII] line flux of F_[CII]=1.11+/-0.10 Jy km/s anda continuum flux density of S_227GHz=0.53+/-0.04 mJy/beam, consistent withprevious unresolved measurements. No other source is detected in continuum or[CII] emission in the field covered by ALMA (~25"). At the resolution of ourALMA observations (0.23", or 1.2 kpc, a factor ~70 smaller beam area comparedto previous measurements), we find that the majority of the emission is verycompact: a high fraction (~80%) of the total line and continuum flux isassociated with a region 1-1.5 kpc in diameter. The remaining ~20% of theemission is distributed over a larger area with radius <4 kpc. The [CII]emission does not exhibit ordered motion on kpc-scales: applying the virialtheorem yields an upper limit on the dynamical mass of the host galaxy of(4.3+/-0.9)x10^10 M_sun, only ~20x higher than the central black hole. Theother targeted lines (CO(2-1), CO(7-6) and [CI]) are not detected, but thelimits of the line ratios with respect to the [CII] emission imply that theheating in the quasar host is dominated by star formation, and not by theaccreting black hole. The star-formation rate implied by the FIR continuum is105-340 M_sun/yr, with a resulting star-formation rate surface density of~100-350 M_sun/yr/kpc^2, well below the value for Eddington-accretion-limitedstar formation.

The compact, ~1 kpc host galaxy of a quasar at z=7.1