  From first principles calculations we find that the nearest and next nearest
neighbor superexchange interactions between Fe ions in LaOFeAs are large,
antiferromagnetic (AF), and give rise to a frustrated magnetic ground state
which consists of two interpenerating AF square sublattices with
M(Fe)=0.48$\mu_B$. The system lowers its energy further by removing the
frustration via a structural distortion. These results successfully explain the
magnetic and structural phase transitions in LaOFeAs recently observed by
neutron scattering. The presence of competing strong antiferromagnetic exchange
interactions and the frustrated ground state suggest that magnetism and
superconductivity in doped LaOFeAs may be strongly coupled, much like in the
high-T$_c$ cuprates.
