  We use four observations with the European VLBI network to measure the first
precise radio parallax of the Crab Pulsar. We found two in-beam extragalactic
sources just outside the Crab Nebula, with one bright enough to use as a
background reference source in our data. We use the Crab Pulsar's giant pulses
to determine fringe and bandpass calibration solutions, which greatly improved
the sensitivity and reliability of our images and allowed us to determine
precise positional offsets between the pulsar and the background source. From
those offsets, we determine a parallax of $\pi=0.53\pm0.06\rm{\;mas}$ and
proper motion of
$(\mu_{\alpha},\mu_{\delta})=(-11.34\pm0.06,2.65\pm0.14)\rm{\;mas\;yr^{-1}}$,
yielding a distance of $d=1.90^{+0.22}_{-0.18}\rm{\;kpc}$ and transverse
velocity of $v_{\perp}=104^{+13}_{-11}\rm{\;km\;s^{-1}}$. These results are
consistent with the Gaia 3 measurements, and open up the possibility of far
more accurate astrometry with further VLBI observations.
