The purpose of this Brief Communication is to calculate the frictional force between two fully ionized plasmas that are moving with respect to one another. Such a calculation is relevant to the expansion of explosion debris into a preionized gas, and to the heating or fueling of a fusion reactor by plasma injection. When the charge densities of the two plasmas are of smilar magnitude, the frictional force is significantly different from that appropriate to the stopping of test particles or to the calculation of electrical conductivity.