In simulations of a 10 PW laser striking a solid, we demonstrate the possibility of producing a pure electron-positron plasma by the same processes as those thought to operate in high-energy astrophysical environments. A maximum positron density of 10(26) m(-3) can be achieved, 7 orders of magnitude greater than achieved in previous experiments. Additionally, 35% of the laser energy is converted to a burst of γ rays of intensity 10(22) W cm(-2), potentially the most intense γ-ray source available in the laboratory. This absorption results in a strong feedback between both pair and γ-ray production and classical plasma physics in the new "QED-plasma" regime.