We examine the possibility that Big Bang Nucleosynthesis (BBN) may produce non-trivial amounts of 6 Li. If a primordial component of this isotope could be observed, it would provide a new fundamental test of Big-Bang cosmology, as well as new constraints on the baryon density of the universe. At present, however, theoretical predictions of the primordial 6 Li abundance are extremely uncertain due to difficulties in both theoretical estimates and experimental determinations of the 2 H(α, γ) 6 Li radiative capture reaction cross-section. We also argue that present observational capabilities do not yet allow the detection of primeval 6 Li in very metal-poor stars of the galactic halo. However, if the critical cross section is towards the upper end of its plausible range, then improvements in 6 Li detection capabilities may allow the establishment of 6 Li as another product of BBN. It is also noted that a primordial 6 Li detection could help resolve current concerns about the extragalactic D/H determination. 26.35.+c,26.44.+h,25.90.+k