The low‐temperature limit to GaAs molecular beam epitaxy (MBE) is studied at temperatures from 250 °C to room temperature. Using transmission electron microscopy of layers grown under a variety of conditions we show that, as for Si MBE, there is an epitaxial thickness hepi at which a growing epitaxial layer becomes amorphous. The temperature, growth rate, composition, and defect density all appear to be constant during growth of the epitaxial layer, and (in analogy with Si MBE) we tentatively associate the breakdown of epitaxy at hepi with roughening of the growth surface. We demonstrate that hepi depends strongly on composition, increasing rapidly with Ga/As ratio at fixed temperature. At fixed Ga/As ratio, hepi shows an abrupt increase from <200 to ≳5000 Å at 210 °C. The results have implications for the growth of GaAs/GaAs for high‐speed photodetectors, as well as possible applications to GaAs/Si heteroepitaxy.