  We report the first measurement of angular correlation parameters in neutron
$\beta$-decay using polarized ultracold neutrons (UCN). We utilize UCN with
energies below about 200 neV, which we guide and store for $\sim 30$ s in a Cu
decay volume. The $\vec{\mu}_n \cdot \vec{B}$ potential of a static 7 T field
external to the decay volume provides a 420 neV potential energy barrier to the
spin state parallel to the field, polarizing the UCN before they pass through
an adiabatic fast passage (AFP) spin-flipper and enter a decay volume, situated
within a 1 T, $2 \times 2\pi$ superconducting solenoidal spectrometer. We
determine a value for the $\beta$-asymmetry parameter $A_0$, proportional to
the angular correlation between the neutron polarization and the electron
momentum, of $A_0 = -0.1138 \pm 0.0051$.
