We report the discovery of a Ly α emitter (LAE) candidate in the immediate foreground of the quasar PSO J158-14 at z _QSO = 6.0685 at a projected distance ∼29 pkpc that is associated with an extremely metal-poor absorption system. This system was found in archival observations of the quasar field with the Very Large Telescope (VLT)/Multi-Unit Spectroscopic Explorer (MUSE) and was previously missed in searches of absorption systems using quasar absorption line spectroscopy, as it imparts no detectable metal absorption lines on the background quasar spectrum. The detected Ly α emission line at a redshift of z _LAE = 6.0323 is well aligned with the outer edge of the quasar’s proximity zone and can plausibly cause its observed damping wing if it is associated with a proximate subdamped Ly α absorption system with a column density of log N HI / cm − 2 ≈ 19.7 . A >10 hr medium-resolution spectrum of the quasar observed with the Magellan/Folded-port InfraRed Echellette (FIRE) and VLT/X-Shooter spectrographs reveals a metallicity constraint of [Z/H] < −3. Such low metallicity makes this system an extremely metal-poor galaxy candidate and provides an exciting site to study possible signatures of Population III stars.