  We measure the 3D kinematic structures of the young stars within the central
0.5 parsec of our Galactic Center using the 10 m telescopes of the W.~M.~Keck
Observatory over a time span of 25 years. Using high-precision measurements of
positions on the sky, and proper motions and radial velocities from new
observations and the literature, we constrain the orbital parameters for each
young star. Our results show two statistically significant sub-structures: a
clockwise stellar disk with 18 candidate stars, as has been proposed before,
but with an improved disk membership; a second, almost edge-on plane of 10
candidate stars oriented East-West on the sky that includes at least one IRS 13
star. We estimate the eccentricity distribution of each sub-structure and find
that the clockwise disk has <$e$> = 0.39 and the edge-on plane has <$e$> =
0.68. We also perform simulations of each disk/plane with incompleteness and
spatially-variable extinction to search for asymmetry. Our results show that
the clockwise stellar disk is consistent with a uniform azimuthal distribution
within the disk. The edge-on plane has an asymmetry that cannot be explained by
variable extinction or incompleteness in the field. The orientation, asymmetric
stellar distribution, and high eccentricity of the edge-on plane members
suggest that this structure may be a stream associated with the IRS 13 group.
The complex dynamical structure of the young nuclear cluster indicates that the
star formation process involved complex gas structures and dynamics and is
inconsistent with a single massive gaseous disk.
