Differential cross sections for Raman scattering between the multiplet levels of the ground electronic state of atomic oxygen are calculated from first principles. The calculated cross sections are in order-of-magnitude agreement with the available experimental measurements. The use of a Raman LIDAR (Light Detection and Ranging) has the potential of giving a three-dimensional map of the density of each of the three fine structure levels of atomic oxygen. Since it was established earlier that the fine structure levels are in local thermodynamic equilibrium (LTE) up to at least 350 km altitude, the Raman LIDAR therefore also has the potential of giving a three-dimensional map of the temperature of the atmosphere.