We present a comprehensive analysis of structure in the young, embedded cluster, NGC 1333 using members identified with Spitzer and 2MASS photometry based on their IR-excess emission. In total, 137 members are identified in this way, composed of 39 protostars and 98 more evolved pre-main sequence stars with disks. Of the latter class, four are transition/debris disk candidates. The fraction of exposed pre-main sequence stars with disks is 83% +/- 11%, showing that there is a measurable diskless pre-main sequence population. The sources in each of the Class I and Class II evolutionary states are shown to have very different spatial distributions relative to the distribution of the dense gas in their natal cloud. However, the distribution of nearest neighbor spacings among these two groups of sources are found to be quite similar, with a strong peak at spacings of 0.045 pc. Radial and azimuthal density profiles and surface density maps computed from the identified YSOs show that NGC 1333 is elongated and not strongly centrally concentrated, confirming previous claims in the literature. We interpret these new results as signs of a low velocity dispersion, extremely young cluster that is not in virial equilibrium.
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