We report the discovery and analysis of only the third Lyman-limit system in which a high-quality resolution , echelle spectrum reveals no metal absorption lines , implying a metallicity \lesssim 1/10000 solar . Our HIRES spectrum of the background quasar , PSS1723 + 2243 , provides a neutral hydrogen column density range for LLS1723 of N _ { \textsc { h \scriptsize { i } } } = 10 ^ { \text { 17.9 - -18.3 } } cm ^ { -2 } at redshift z _ { \textrm { \scriptsize abs } } \approx 4.391 . The lower bound on this range , and the lack of detectable absorption from the strongest low-ionisation metal lines , are combined in photoionisation models to infer a robust , conservative upper limit on the metallicity : \log ( Z / Z _ { \odot } ) < -4.14 at 95 % confidence . Such a low metallicity raises the question of LLS1723 ’ s origin and enrichment history . Previous simulations of the circumgalactic medium imply that LLS1723 is a natural candidate for a cold gas stream accreting towards a galaxy . Alternatively , LLS1723 may represent a high-density portion of the intergalactic medium containing either pristine gas – unpolluted by stellar debris for 1.4 Gyr after the Big Bang – or the remnants of low-energy supernovae from ( likely low-mass ) Population III stars . Evidence for the circumgalactic scenario could be obtained by mapping the environment around LLS1723 with optical integral-field spectroscopy . The intergalactic possibilities highlight the need for – and opportunity to test – simulations of the frequency with which such high-density , very low-metallicity systems arise in the intergalactic medium .