  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 1 mm. A time measurement at this
precision level will also be of interest beyond the LHC and beyond high energy
particle physics. We present in this paper 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.
