There are currently two cosmological lithium problems: compared with predictions from Big Bang Nucleosynthesis and models for Galactic cosmic ray production, the observed 7Li abundance in Galactic halo stars is too low while the 6Li content is too high. Here we report on new Keck/HIRES observations of the two extremely metal-poor stars G064-012 and G064-37, which both show distortions of the Li I 670.8 nm line consistent with a significant (≈3σ) presence of 6Li. If confirmed, these are the lowest metallicity 6Li detections and would suggest a cosmological or pre-Galactic origin for the isotope. Invoking stellar Li depletion to solve the above-mentioned 7Li discrepancy would further increase the inferred initial 6Li abundance by a factor of ...