We introduce Maxwell's equations with chiral constitutive equations in the
form given by Fedorov and Bokut. In the case where the scatterer is an infi
nitely long cylinder we derive a two-dimensional scattering problem and dis
cuss the existence and uniqueness of solutions via an integral equation app
roach. Then we formulate the inverse scattering problem to find the shape o
f the scatterer if the far-field data are known. We give a uniqueness resul
t and describe a numerical reconstruction scheme.