  Motivated by the recent discovery of iron-based superconductors, with high
critical temperatures and multiple bands crossing the Fermi level, we address
the conditions for the presence of chiral superconducting phases configurations
in the in-plane magnetic field vs. temperature phase diagram of a quasi-2D
frustrated three-band superconductor. Due to Zeeman splitting, the coupled
superconducting gap equations present a complex set of solutions. For weak
interband couplings, chiral configurations are only attained in a narrow strip
of the in-plane magnetic field vs. temperature phase diagram. This strip of
chiral states becomes narrower and disappears at low temperatures, giving way
to a first-order transition between non-chiral superconducting states. For
stronger interband couplings, the chiral strip is much broader, if the
interband couplings are approximately equal; otherwise, the chiral region is
expected to be completely absent of the phase diagram.
