  We present measurements of the dynamical structure factor $S(q,\omega)$ of an
interacting one-dimensional (1D) Fermi gas for small excitation energies. We
use the two lowest hyperfine levels of the $^6$Li atom to form a
pseudo-spin-1/2 system whose s-wave interactions are tunable via a Feshbach
resonance. The atoms are confined to 1D by a two-dimensional optical lattice.
Bragg spectroscopy is used to measure a response of the gas to density
("charge") mode excitations at a momentum $q$ and frequency $\omega$. The
spectrum is obtained by varying $\omega$, while the angle between two laser
beams determines $q$, which is fixed to be less than the Fermi momentum
$k_\textrm{F}$. The measurements agree well with Tomonaga-Luttinger theory.
