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In this letter, we report on up to 300-Gb/s real-time all-fiber-based optical eye-diagram measurements with 1.6-ps temporal resolution and 5-Hz refresh rate by all-optical sampling using parametric amplification in a short (50 m) highly nonlinear fiber. This represents, to the best of our knowledge, the highest bit-rate eye-diagram measurement so far, as well as the first demonstration of a fiber-based eye analyzer. The sensitivity and operational optical bandwidth is comparable to previously reported state-of-the-art nonlinear crystal-based sampling systems. We believe our results show that fiber-based optical sampling is indeed a potential candidate for characterization of future ultrahigh bit-rate optical communication systems.