The planned luminosity increase at the Large Hadron Collider in the coming years has triggered interest in the use of the particles’ time of arrival as additional information in specialized detectors to mitigate the impact of pile-up. The required time resolution is of the order of tens of picoseconds, with a spatial granularity of the order of 1mm. A time measurement at this precision level will also be of interest beyond the LHC and beyond high energy particle physics. We present the first developments towards a radiation hard Depleted Monolithic Active Pixel Sensor (DMAPS), with high-resolution time measurement capability. The technology chosen is a standard high voltage CMOS process, in conjunction with a high resistivity detector material, which has already proven to efficiently detect particles in tracking applications after several hundred of Mrad of irradiation.