Distributed measurement of forward stimulated Brillouin scattering (FSBS) attracted substantial attention for its ability to probe media surrounding optical fibers. Currently, all techniques extract the information from the FSBS-induced local energy transfer among distinct optical tones, this transfer being fundamentally sensitive to intensity perturbations imposed by nonlinear effects. Instead, here we propose to extract the local FSBS information by measuring the frequency shift of a short optical pulse subject to the phase chirp modulation caused by harmonic FSBS oscillation. In full contrast with existing techniques, the optical pulse is much shorter than the period of the acoustic oscillation, enabling ultrashort spatial resolutions, and its frequency shift is precisely probed by a standard Brillouin optical time-domain analyzer. The proposed technique is validated in both remote and integrally distributed sensing configurations, demonstrating spatial resolutions of 0.8 m and 2 m, respectively, substantially outperforming state-of-the-art techniques.