The Crab Nebula is the brightest TeV gamma-ray source in the sky and has been used for the past 25 years as a reference source in TeV astronomy, for calibration and verification of new TeV instruments. The High Altitude Water Cherenkov Observatory (HAWC), completed in early 2015, has been used to observe the Crab Nebula at high significance across nearly the full spectrum of energies to which HAWC is sensitive. HAWC is unique for its wide field of view, nearly 2 sr at any instant, and its high-energy reach, up to 100 TeV. HAWC's sensitivity improves with the gamma-ray energy. Above ∼1 TeV the sensitivity is driven by the best background rejection and angular resolution ever achieved for a wide-field ground array. We present a time-integrated analysis of the Crab using 507 live days of HAWC data from 2014 November to 2016 June. The spectrum of the Crab is fit to a function of the form φ(E)= φ0(E/E0)-α-β In(E/E0). The data is well fitted with values of α = 2.63 ±0.03, β = 0.15 ±0.03, and log10(φ0cm2s TeV)=-12.60±0.02 when E 0 is fixed at 7 TeV and the fit applies between 1 and 37 TeV. Study of the systematic errors in this HAWC measurement is discussed and estimated to be ±50% in the photon flux between 1 and 37 TeV. Confirmation of the Crab flux serves to establish the HAWC instrument's sensitivity for surveys of the sky. The HAWC all-sky survey will be the deepest survey of the northern sky ever conducted in the multi-TeV band.