In this Letter, the mesoscopic voltage and conductance fluctuations of a Luttinger liquid are examined. For quasiballistic wires, one finds that the amplitude of conductance fluctuations, i.e., $\mathrm{Var}(G)$, is proportional to ${T}^{4g\ensuremath{-}5}$ where $g\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}\ensuremath{\Elzxh}v(\ensuremath{\partial}n/\ensuremath{\partial}\ensuremath{\mu})$ is a dimensionless measure of compressibility. For macroscopic wires, one finds resistance fluctuations of the form $\mathrm{Var}(R)\ensuremath{\sim}{T}^{4g\ensuremath{-}5}$. We also investigate the voltage distribution function and the length scale over which self-averaging occurs.