  We suggest an experiment to study Luttinger liquid behavior in a
one-dimensional nanostructure, avoiding the usual complications associated with
transport measurements. The proposed setup consists of a quantum box, biased by
a gate voltage, and side-coupled to a quantum wire by a point contact. Close to
the degeneracy points of the Coulomb blockaded box, and in the presence of a
magnetic field sufficiently strong to spin polarize the electrons, the setup
can be described as a Luttinger liquid interacting with an effective Kondo
impurity. Using exact nonperturbative techniques we predict that the
differential capacitance of the box will exhibit distinctive Luttinger liquid
scaling with temperature and gate voltage.
