The epitaxial growth of CeO2 films on SrTiO3(001) has been investigated over a wide range of growth parameters using oxygen-plasma-assisted molecular beam epitaxy. The lattice mismatch for CeO2 on SrTiO3(001) is 2.0% (compressive) if the film nucleates with a 45 degrees rotation about [001] relative to the substrate (i.e., CeO2(001)\\SrTiO3(001) and CeO2[110]\\SrTiO3[100]). pure-phase, single-crystalline epitaxial films of CeO2(001) with the above epitaxial relationship readily grew on SrTiO3(001) for substrate temperatures ranging from 550 to 700 degrees C. However, small amounts of (111) and (220) minority orientations also nucleated at the higher substrate temperatures. In addition, the film surface was observed to become progressively smoother with increasing substrate temperature due to more extensive island agglomeration. The highest-quality him surface grown at 700 degrees C is unreconstructed and oxygen terminated.