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Firn from an ice cave in the highest mountain of Greece, Mount Olympus, was sampled and analyzed to determine the tritium content in order to estimate rates of accumulation and to date the ice plug. The presence of a sharp raise of tritium content indicating the nuclear testing era was expected to be preserved into ice beds. Tritium concentrations were found to vary from 0.9 to 11 TU. This peak did not appear in the analyzed samples, providing an upper age limit of less than 50 years for the oldest sampled layer. It is suggested that the rate of melting is responsible for the absence of older firn layers.