Alexander Fleming, a Scottish scientist, is credited with discovering the first antibiotic, penicillin. In 1928, he noticed that bacteria could not survive on a plate that contained a mold commonly found on bread. He went on to show that the effect was due to a diffusible substance made by the mold. However, penicillin was not available to the general public until the early 1940s when scientists learned how to produce and purify large amounts of penicillin.
In fact, technically speaking, Fleming may have rediscovered a substance that had been found before. In 1896, the French medical student Ernest Duchesne showed antibiotic properties of the mold Penicillium, but did not report a connection between the fungus and a substance that had antibacterial properties. Penicillium was unknown to the scientific community until Fleming discovered the phenomenon and the substance, and named it penicillin.
In 1895, there was a report by an Italian researcher, Vincenzo Tiberio, describing a natural substance from molds which had antibacterial properties resembling penicillin. Yet another report describes a professor at John Hopkins University in Baltimore who showed his students an agar plate with a mold which inhibited bacterial growth. (Levy, S.B. The Antibiotic Paradox. How Misuse of Antibiotics Destroys Their Curative Powers. Perseus Books, 2002). So perhaps others had seen and described the phenomenon, but Fleming was the first to bring such a substance to wide scientific attention.