Inelastic light-scattering spectra of underdoped La2-xSrxCuO4 single crystals are presented which provide direct evidence of the formation of quasi-one-dimensional charged structures in the two-dimensional CuO2 planes. The stripes manifest themselves in a Drude-like peak at low energies and temperatures. The selection rules allow us to determine the orientation to be along the diagonals at x=0.02 and along the principal axes at x=0.10. The electron-lattice interaction determines the correlation length which turns out to be larger in compound classes with lower superconducting transition temperatures. Temperature is the only scale of the response at different doping levels demonstrating the importance of quantum critical behavior.