  CTA (Cherenkov Telescope Array) is the next generation ground-based
observatory for gamma-ray astronomy at very-high energies. The Large-Sized
Telescope prototype (LST-1) is located at the Northern site of CTA, 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 $\simeq 20$ GeV.
LST-1 started performing astronomical observations in November 2019, during its
commissioning phase, and it has been taking data since then. 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 basic performance parameters of the telescope. The data sample consists of
around 36 hours of observations at low zenith angles collected between November
2020 and March 2022. 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 behavior. The energy threshold at trigger
level is estimated to be around 20 GeV, rising to $\simeq 30$ 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
0.12 to 0.40 degrees, and energy resolution from 15 to 50%. Flux sensitivity is
around 1.1% of the Crab Nebula flux above 250 GeV for a 50-h 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.
