The primordial abundances of light elements produced in the standard theory of Big Bang nucleosynthesis (BBN) depend only on the cosmic ratio of baryons to photons, a quantity inferred from observations of the microwave background. The predicted primordial (7)Li abundance is four times that measured in the atmospheres of Galactic halo stars. This discrepancy could be caused by modification of surface lithium abundances during the stars' lifetimes or by physics beyond the Standard Model that affects early nucleosynthesis. The lithium abundance of low-metallicity gas provides an alternative constraint on the primordial abundance and cosmic evolution of lithium that is not susceptible to the in situ modifications that may affect stellar atmospheres. Here we report observations of interstellar (7)Li in the low-metallicity gas of the Small Magellanic Cloud, a nearby galaxy with a quarter the Sun's metallicity. The present-day (7)Li abundance of the Small Magellanic Cloud is nearly equal to the BBN predictions, severely constraining the amount of possible subsequent enrichment of the gas by stellar and cosmic-ray nucleosynthesis. Our measurements can be reconciled with standard BBN with an extremely fine-tuned depletion of stellar Li with metallicity. They are also consistent with non-standard BBN.