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.
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