We report the first dark matter search results from XENON1T, a $sim$2000-kg-target-mass dual-phase (liquid-gas) xenon time projection chamber in operation at the Laboratori Nazionali del Gran Sasso in Italy and the first ton-scale detector of this kind. The blinded search used 34.2 live days of data acquired between November 2016 and January 2017. Inside the (1042$pm$12) kg fiducial mass and in the [5, 40] $mathrm{keV}_{mathrm{nr}}$ energy range of interest for WIMP dark matter searches, the electronic recoil background was $(1.93 pm 0.25) times 10^{-4}$ events/(kg $times$ day $times mathrm{keV}_{mathrm{ee}}$), the lowest ever achieved in a dark matter detector. A profile likelihood analysis shows that the data is consistent with the background-only hypothesis. We derive the most stringent exclusion limits on the spin-independent WIMP-nucleon interaction cross section for WIMP masses above 10 GeV/c${}^2$, with a minimum of 7.7 $times 10^{-47}$ cm${}^2$ for 35-GeV/c${}^2$ WIMPs at 90% confidence level.
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