  We present an investigation of the spectral and spatial structure of the
X-ray emission from 3C 58 based on a 350 ks observation with the Chandra X-ray
Observatory. This deep image, obtained as part of the Chandra Large Project
program, reveals new information on nearly all spatial scales in the pulsar
wind nebula (PWN). On the smallest scales we derive an improved limit of T <
1.02 X 10^6 K for blackbody emission from the entire surface of the central
neutron star (NS), confirming the need for rapid, nonstandard cooling in the
stellar interior. Furthermore, we show that the data are consistent with
emission from a light element atmosphere with a similar temperature.
Surrounding the NS, a toroidal structure with a jet is resolved, consistent
with earlier measurements and indicative of an east-west orientation for the
projected rotation axis of the pulsar. A complex of loop-like X-ray filaments
fills the nebula interior, and corresponds well with structures seen in the
radio band. Several of the structures coincide with optical filaments as well.
The emission from the interior of the PWN, including the pulsar, jet, and
filaments, is primarily nonthermal in nature. The power law index steepens with
radius, but appears to also show small azimuthal variations. The outermost
regions of the nebula require a thermal emission component, confirming the
presence of an ejecta-rich swept up shell.
