The notion of Electromagnetic Chirality, recently introduced in the Physics literature,
is investigated in the framework of scattering of time-harmonic electromagnetic waves by
bounded scatterers. This type of chirality is defined as a property of the far field operator.
The relation of this novel notion of chirality to that of geometric chirality of the scatterer
is explored. It is shown for several examples of scattering problems that electromagnetic
achirality is a more general property than geometric chirality. On the other hand, a
chiral material law, as for example given by the Drude-Born-Fedorov model, yields an
electromagnetically chiral scatterer. Electromagnetic chirality also allows the definition
of a measure. Scatteres invisible to fields of one helicity turn out to be maximally chiral
with respect to this measure. For a certain class of electromagnetically chiral scatters, we
provide numerical calculations of the measure of chirality through solutions of scattering
problems computed by a boundary element method.