  The XENON1T experiment is currently in the commissioning phase at the
Laboratori Nazionali del Gran Sasso, Italy. In this article we study the
experiment's expected sensitivity to the spin-independent WIMP-nucleon
interaction cross section, based on Monte Carlo predictions of the electronic
and nuclear recoil backgrounds.
  The total electronic recoil background in $1$ tonne fiducial volume and ($1$,
$12$) keV electronic recoil equivalent energy region, before applying any
selection to discriminate between electronic and nuclear recoils, is $(1.80 \pm
0.15) \cdot 10^{-4}$ ($\rm{kg} \cdot day \cdot keV)^{-1}$, mainly due to the
decay of $^{222}\rm{Rn}$ daughters inside the xenon target. The nuclear recoil
background in the corresponding nuclear recoil equivalent energy region ($4$,
$50$) keV, is composed of $(0.6 \pm 0.1)$ ($\rm{t} \cdot y)^{-1}$ from
radiogenic neutrons, $(1.8 \pm 0.3) \cdot 10^{-2}$ ($\rm{t} \cdot y)^{-1}$ from
coherent scattering of neutrinos, and less than $0.01$ ($\rm{t} \cdot y)^{-1}$
from muon-induced neutrons.
  The sensitivity of XENON1T is calculated with the Profile Likelihood Ratio
method, after converting the deposited energy of electronic and nuclear recoils
into the scintillation and ionization signals seen in the detector. We take
into account the systematic uncertainties on the photon and electron emission
model, and on the estimation of the backgrounds, treated as nuisance
parameters. The main contribution comes from the relative scintillation
efficiency $\mathcal{L}_\mathrm{eff}$, which affects both the signal from WIMPs
and the nuclear recoil backgrounds. After a $2$ y measurement in $1$ t fiducial
volume, the sensitivity reaches a minimum cross section of $1.6 \cdot 10^{-47}$
cm$^2$ at m$_\chi$=$50$ GeV/$c^2$.
