We report the observation of reflection high‐energy diffraction (RHEED) intensity oscillations during the growth of GaAs using triethylgallium in chemical beam epitaxy (CBE). The oscillation period corresponds exactly to the time required for the growth of one monolayer. RHEED oscillation studies also suggest the absence of flux transients due to switching of gas flows, abrupt and complete initiation and termination of growth with submonolayer resolution, and that CBE is capable of thickness control with submonolayer precision when coupled with the use ofinsituRHEED intensity monitoring technique. The temperature and flux dependence of growth rates are also studied using RHEED oscillations. Results indicate that CBE growth is predominantly via a two‐dimensional layer‐by‐layer mechanism.