At timescales once deemed immeasurably small by Einstein, the random movement of Brownian particles in a liquid is expected to be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation fast and precise enough to capture this motion. Here we report the observation of the Brownian motion of a single particle in an optical trap with 75 MHz bandwidth and sub-angstrom spatial precision and the determination of the particle's velocity autocorrelation function. Our observation is the first measurement of ballistic Brownian motion of a particle in a liquid. The data are in excellent agreement with theoretical predictions taking into account the inertia of the particle and hydrodynamic memory effects.