  We introduce a definition of the electromagnetic chirality of an object and
show that it has an upper bound. Reciprocal objects attain the upper bound if
and only if they are transparent for all the fields of one polarization
handedness (helicity). Additionally, electromagnetic duality symmetry, i.e.,
helicity preservation upon interaction, turns out to be a necessary condition
for reciprocal objects to attain the upper bound. We use these results to
provide requirements for the design of such extremal objects. The requirements
can be formulated as constraints on the polarizability tensors for dipolar
objects or on the material constitutive relations for continuous media. We also
outline two applications for objects of maximum electromagnetic chirality: a
twofold resonantly enhanced and background-free circular dichroism measurement
setup, and angle-independent helicity filtering glasses. Finally, we use the
theoretically obtained requirements to guide the design of a specific
structure, which we then analyze numerically and discuss its performance with
respect to maximal electromagnetic chirality.
