  We use the Gutzwiller variational theory to calculate the ground-state phase
diagram and quasi-particle bands of LaOFeAs. The Fe3d--As4p Wannier-orbital
basis obtained from density-functional theory defines the band part of our
eight-band Hubbard model. The full atomic interaction between the electrons in
the iron orbitals is parameterized by the Hubbard interaction U and an average
Hund's-rule interaction J. We reproduce the experimentally observed small
ordered magnetic moment over a large region of (U,J) parameter space. The
magnetically ordered phase is a stripe spin-density wave of quasi-particles.
