The magnetic properties of the ground state of a low-density free-electron gas in three dimensions have been the subject of theoretical speculation and controversy for seven decades(1). Not only is this a difficult theoretical problem to solve, it is also a problem which has not hitherto been directly addressed experimentally. Here we report measurements on electron-doped calcium hexaboride (CaB6) which, we argue, show that-at a density of 7 x 10(19) electrons cm(-3)-the ground state is ferromagnetically polarized with a saturation moment of 0.07 mu(B) per electron. Surprisingly, the magnetic ordering temperature of this itinerant ferromagnet is 600 K, of the order of the Fermi temperature of the electron gas.