Low gain avalanche detectors can measure charged particle fluences with high speed and spatial precision, and are a promising technology for radiation monitoring and dosimetry. A detector has been tested in a medical linac where single particles were observed with a time resolution of 50 ps. The integrated response is similar to a standard ionising chamber but with a spatial precision twenty times finer, and a temporal precision over 100 million times better, with the capability to measure the charge deposited by a single linac pulse. The unprecedented resolving power allows the structure of the ∼3 μs linac pulses to be viewed and the 350 ps sub-pulses in the train to be observed.