Brillouin optical time-domain analysis (BOTDA) requires frequency mapping of the Brillouin spectrum to obtain environmental information (e.g., temperature or strain) over the length of the sensing fiber, with the finite frequency-sweeping time-limiting applications to only static or slowly varying strain or temperature environments. To solve this problem, we propose the use of an optical chirp chain probe wave to remove the requirement of frequency sweeping for the Brillouin spectrum, which enables distributed ultrafast strain measurement with a single pump pulse. The optical chirp chain is generated using a frequency-agile technique via a fast-frequency-changing microwave, which covers a larger frequency range around the Stokes frequency relative to the pump wave, so that a distributed Brillouin gain spectrum along the fiber is realized. Dynamic strain measurements for periodic mechanical vibration, mechanical shock, and a switch event are demonstrated at sampling rates of 25 kHz, 2.5 MHz and 6.25 MHz, respectively. To the best of our knowledge, this is the first demonstration of distributed Brillouin strain sensing with a wide-dynamic range at a sampling rate of up to the MHz level.