We describe a novel method of single-shot trap frequency measurement for a confined Bose-Einstein Condensate, which uses an atom laser to repeatedly sample the mean velocity of trap oscillations as a function of time. The method is able to determine the trap frequency to an accuracy of 39 ppm (16 mHz) in a single experimental realization, improving on the literature by a factor of three. Further, we show that by employing a reconstructive aliasing approach our method can be applied to trap frequencies more than a factor of 3 greater than the sampling frequency.