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, $2 times 2pi$ 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 $A_0 = -0.1138 pm 0.0051$.