We measure up to 2x10;{10} positrons per steradian ejected out the back of approximately mm thick gold targets when illuminated with short ( approximately 1 ps) ultraintense ( approximately 1x10;{20} W/cm;{2}) laser pulses. Positrons are produced predominately by the Bethe-Heitler process and have an effective temperature of 2-4 MeV, with the distribution peaking at 4-7 MeV. The angular distribution of the positrons is anisotropic. Modeling based on the measurements indicate the positron density to be approximately 10;{16} positrons/cm;{3}, the highest ever created in the laboratory.