The Cherenkov Telescope Array (CTA) is a next-generation ground-based observatory for gamma-ray astronomy at very high energies. The Large-Sized Telescope prototype (LST-1) is located at the CTA-North site, on the Canary Island of La Palma. LSTs are designed to provide optimal performance in the lowest part of the energy range covered by CTA, down to similar or equal to 20 GeV. LST-1 started performing astronomical observations in 2019 November, during its commissioning phase, and it has been taking data ever since. We present the first LST-1 observations of the Crab Nebula, the standard candle of very-high-energy gamma-ray astronomy, and use them, together with simulations, to assess the performance of the telescope. LST-1 has reached the expected performance during its commissioning period-only a minor adjustment of the preexisting simulations was needed to match the telescope's behavior. The energy threshold at trigger level is around 20 GeV, rising to similar or equal to 30 GeV after data analysis. Performance parameters depend strongly on energy, and on the strength of the gamma-ray selection cuts in the analysis: angular resolution ranges from 0.degrees 12-0.degrees 40, and energy resolution from 15%-50%. Flux sensitivity is around 1.1% of the Crab Nebula flux above 250 GeV for a 50 hr observation (12% for 30 minutes). The spectral energy distribution (in the 0.03-30 TeV range) and the light curve obtained for the Crab Nebula agree with previous measurements, considering statistical and systematic uncertainties. A clear periodic signal is also detected from the pulsar at the center of the Nebula.
