The most massive and complex globular clusters in the Galaxy are thought to have originated as the nuclear cores of now tidally disrupted dwarf galaxies, but the connection between globular clusters and dwarf galaxies is tenuous with the M54/Sagittarius system representing the only unambiguous link. The globular cluster Omega Centauri ({omega}Cen) is more massive and chemically diverse than M54, and is thought to have been the nuclear star cluster of either the Sequoia or Gaia-Enceladus galaxy. Local Group dwarf galaxies with masses equivalent to these systems often host significant populations of very metal-poor stars ([Fe/H]<-2.5), and one might expect to find such objects in {omega}Cen. Using high-resolution spectra from Magellan-M2FS, we detected 11 stars in a targeted sample of 395 that have [Fe/H] ranging from -2.30 to -2.52. These are the most metal-poor stars discovered in the cluster, and are five times more metal-poor than {omega}Cen's dominant population. However, these stars are not so metal-poor as to be unambiguously linked to a dwarf galaxy origin. The cluster's metal-poor tail appears to contain two populations near [Fe/H]~-2.1 and -2.4, which are very centrally concentrated but do not exhibit any peculiar kinematic signatures. Several possible origins for these stars are discussed.