  We propose an explanation for the electronic nematic state observed recently
in parent iron-based superconductors [T.-M. Chuang et al., Science 327, 181
(2010)]. We argue that the quasi-one-dimensional nanostructure identified in
the quasiparticle interference (QPI) is a consequence of the interplay of the
magnetic ($\pi$, 0) spin-density wave (SDW) order with the underlying
electronic structure. We show that the evolution of the QPI peaks largely
reflects quasiparticle scattering between electronic bands involved in the SDW
formation. Because of the ellipticity of the electron pocket and the fact that
only one of the electron pockets is involved in the SDW, the resulting QPI has
a pronounced one-dimensional structure. We further predict that the QPI crosses
over to two-dimensionality on an energy scale, set by the SDW gap, which we
estimate from neutron scattering data to be around 90 meV.
