Low-energy, dark excitonic states have recently been predicted to lie below the first bright (E11) exciton in semiconducting single-walled carbon nanotubes [Phys. Rev. Lett. 93, 157402 (2004)10.1103/PhysRevLett.93.157402]. Decay into such deep excitonic states is implicated as a mechanism which reduces photoluminescence quantum yields. In this study we report the first direct observation of deep excitons in SWNTs. Photoluminescence (PL) microscopy of suspended semiconducting single-walled carbon nanotubes (SWNTs) reveals weak emission satellites redshifted by approximately 38-45 and approximately 100-130 meV relative to the main E11 PL emission peaks. Similar satellites, redshifted by 95-145 meV depending on nanotube species, were also found in PL measurements of ensembles of SWNTs in water-surfactant dispersions. The relative intensities of these deep exciton emission features depend on the nanotube surroundings.