  We present a quantitative, empirically based argument that at least some
Class I sources are low-mass, pre-main-sequence stars surrounded by spatially
extended envelopes of dusty gas. The source luminosity arises principally from
stellar gravitational contraction, as in optically visible pre-main-sequence
stars that lack such envelopes. We base our argument on the fact that some
Class I sources in Orion and other star-forming regions have been observed by
Spitzer to be periodic variables in the mid-infrared, and with periods
consistent with T Tauri rotation rates. Using a radiative transfer code, we
construct a variety of dust envelopes surrounding rotating, spotted stars, to
see if an envelope that produces a Class I SED at least broadly matches the
observed modulations in luminosity. Acceptable envelopes can either be
spherical or flattened, and may or may not have polar cavities. The key
requirement is that they have a modest equatorial optical depth at the Spitzer
waveband of 3.6 ${\mu}$m, typically ${\tau_{3.6}}$ ${\approx}$ 0.6. The total
envelope mass, based on this limited study, is at most about 0.1
$\text{M}_{\odot}$, less than a typical stellar mass. Future studies should
focus on the dynamics of the envelope, to determine whether material is
actually falling onto the circumstellar disk.
