We use Spitzer Space Telescope observations from the Spitzer Survey of the Small Magellanic Cloud (S3MC) to study the young stellar content of N66, the largest and brightest HII region in the SMC. In addition to large numbers of normal stars, we detect a significant population of bright, red infrared sources that we identify as likely to be young stellar objects (YSOs). We use spectral energy distribution (SED) fits to classify objects as ordinary (main sequence or red giant) stars, asymptotic giant branch stars, background galaxies, and YSOs. This represents the first large-scale attempt at blind source classification based on Spitzer SEDs in another galaxy. We firmly identify at least 61 YSOs, with another 50 probable YSOs; only one embedded protostar in the SMC was reported in the literature prior to the S3MC. We present color selection criteria that can be used to identify a relatively clean sample of YSOs with IRAC photometry. Our fitted SEDs indicate that the infrared-bright YSOs in N66 have stellar masses ranging from 2 Msun to 17 Msun, and that approximately half of the objects are Stage II protostars, with the remaining YSOs roughly evenly divided between Stage I and Stage III sources. We find evidence for primordial mass segregation in the HII region, with the most massive YSOs being preferentially closer to the center than lower-mass objects. Despite the low metallicity and dust content of the SMC, the observable properties of the YSOs appear consistent with those in the Milky Way. Although the YSOs are heavily concentrated within the optically bright central region of N66, there is ongoing star formation throughout the complex and we place a lower limit on the star formation rate of 3.2 x 10^-3 Msun/yr over the last ~1 Myr.
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