A new technique is described for the isochoric heating (i.e., heating at constant volume) of matter to high energy-density plasma states (>10(5) J/g) on a picosecond time scale (10(-12)sec). An intense, collimated, ultrashort-pulse beam of protons--generated by a high-intensity laser pulse--is used to isochorically heat a solid density material to a temperature of several eV. The duration of heating is shorter than the time scale for significant hydrodynamic expansion to occur; hence the material is heated to a solid density warm dense plasma state. Using spherically shaped laser targets, a focused proton beam is produced and used to heat a smaller volume to over 20 eV. The technique described of ultrafast proton heating provides a unique method for creating isochorically heated high-energy density plasma states.