  We present new Atacama Large Millimeter/Submillimeter Array (ALMA) 850um
continuum observations of the original Lyman-alpha Blob (LAB) in the SSA22
field at z=3.1 (SSA22-LAB01). The ALMA map resolves the previously identified
submillimeter source into three components with total flux density S_850 =
1.68+/-0.06 mJy, corresponding to a star formation rate of ~150 M_sun/yr. The
submillimeter sources are associated with several faint (m~27 mag) rest-frame
ultraviolet sources identified in Hubble Space Telescope Imaging Spectrograph
(STIS) clear filter imaging (~5850A). One of these companions is
spectroscopically confirmed with Keck MOSFIRE to lie within 20 projected kpc
and 250 km/s of one of the ALMA components. We postulate that some of these
STIS sources represent a population of low-mass star-forming satellites
surrounding the central submillimeter sources, potentially contributing to
their growth and activity through accretion. Using a high resolution
cosmological zoom simulation of a 10^13 M_sun halo at z=3, including stellar,
dust and Ly-alpha radiative transfer, we can model the ALMA+STIS observations
and demonstrate that Ly-alpha photons escaping from the central submillimeter
sources are expected to resonantly scatter in neutral hydrogen, the majority of
which is predicted to be associated with halo substructure. We show how this
process gives rise to extended Ly-alpha emission with similar surface
brightness and morphology to observed giant LABs.
