Through a systematic search of all layered bulk compounds combined with density functional calculations employing hybrid exchange-correlation functionals, we predict a family of three magnetic two-dimensional (2D) materials with half-metallic band structures. The 2D materials, FeCl, FeBr, and FeI, are all sufficiently stable to be exfoliated from bulk layered compounds. The Fe ions in these materials are in a high-spin octahedral d configuration leading to a large magnetic moment of 4 μ. Calculations of the magnetic anisotropy show an easy-plane for the magnetic moment. A classical XY model with nearest neighbor coupling estimates critical temperatures, T, for the Berezinskii-Kosterlitz-Thouless transition ranging from 122 K for FeI to 210 K for FeBr. The quantum confinement of these 2D materials results in unusually large spin gaps, ranging from 4.0 eV for FeI to 6.4 eV for FeCl, which should defend against spin current leakage even at small device length scales. Their purely spin-polarized currents and dispersive interlayer interactions should make these materials useful for 2D spin valves and other spintronic applications.