Simultaneous acceleration of hundreds of dust particles to hypervelocities by collimated plasma flows ejected from a coaxial gun is demonstrated. Graphite and diamond grains with radii between 5 and 30 microm, and flying at speeds up to 3.7 km/s, have been recorded with a high-speed camera. The observations agree well with a model for plasma-drag acceleration of microparticles much larger than the plasma screening length.