A very large oxygen-isotope shift of the charge-stripe ordering temperature in the high-temperature superconductors La_2-xSr_xCuO₄ has been observed using x-ray absorption spectroscopy, a fast (~10^-15 seconds) and local probe (~5 Å). Upon replacing ¹⁶O with ¹⁸O, the charge-stripe ordering temperature in La_1.94Sr_0.06CuO₄ increases from about 110 K to 180 K. The present results provide compelling evidence for a strong electron-phonon interaction in this compound, and thus place important constraints on the microscopic origin of the stripe formation.