The paper is devoted to the implementation of the linear sampling method, in the framework of the inverse scattering problem, to the problem of reconstruction of the boundary of a chiral obstacle, which is assumed to be an infinite cylinder (thus, the problem is two-dimensional). The constitutive relations for the chiral medium are taken in the Drude-Born-Fedorov form. In order to justify the linear sampling method, the authors analyse the associated interior transmission problem, establish the corresponding far field equation and prove its solvability.