  Using an ultra-deep blind survey with the MUSE integral field spectrograph on
the ESO Very Large Telescope, we obtain spectroscopic redshifts to a depth
never explored before: galaxies with observed magnitudes m > 30 - 32.
Specifically, we detect objects via Lyman-alpha emission at 2.9 < z < 6.7
without individual continuum counterparts in areas covered by the deepest
optical/near-infrared imaging taken by the Hubble Space Telescope, the Hubble
Ultra Deep Field. In total, we find 102 such objects in 9 square arcminutes at
these redshifts. Detailed stacking analyses confirm the Lyman-alpha emission as
well as the 1216 Angstrom-breaks and faint UV continua (M_UV ~ -15). This makes
them the faintest spectroscopically-confirmed objects at these redshifts,
similar to the sources believed to reionize the universe. A simple model for
the expected fraction of detected/undetected Lyman-alpha emitters as a function
of luminosity is consistent with these objects being the high-equivalent width
tail of the normal Lyman-alpha-emitter population at these redshifts.
