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 \times 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 .