The prospect of pileup induced backgrounds at the High Luminosity LHC (HL-LHC) has stimulated intense interest in developing technologies for charged particle detection with accurate timing at high rates. The required accuracy follows directly from the nominal interaction distribution within a bunch crossing (sigma(2) similar to 5 cm, sigma(t) similar to 170 ps). A time resolution of the order of 20-30 ps would lead to significant reduction of these backgrounds. With this goal, we present a new detection concept called PICOSEC, which is based on a "two-stage'' Micromegas detector coupled to a Cherenkov radiator and equipped with a photocathode. First results obtained with this new detector yield a time resolution of 24 ps for 150 GeV muons, and 76 ps for single photoelectrons.