The - 1 6 O- 1 8 O oxygen isotope effect has been studied in the Raman spectra of single crystals of the high-T c superconductor Bi 2 Sr 2 CaCu 2 O 8 + δ . It is found that the oxygen isotope shifts of all of the vibrational peaks fall into one of three narrow ranges. The absence of a significant isotope shift for certain peaks indicates either that they correspond to normal modes that involve only the motion of cations (peaks at and below 181 cm - 1 ), or that they involve the vibration of oxygen on sites where isotope exchange proceeds extremely slowly (peaks at 310 cm - 1 and 661 cm - 1 ). The isotope-shift data provide strong evidence that, contrary to previous assignments, the A 1 g peaks at 287 cm - 1 and 350 cm - 1 correspond to vibrational modes of oxygen atoms in the copper layer. Large oxygen isotope shifts support the assignment of the 386 cm - 1 peak to in-plane vibrations of oxygen atoms in the strontium layer, and of the 458 cm - 1 peak to c-axis vibrations of these same atoms. They are inconsistent with an earlier suggestion that the 458 cm - 1 peak corresponds to a vibrational mode of oxygen atoms in the copper layer.