The basic growth mode of a thin epitaxial cuprate film ( < 200 Angstrom) on a given substrate depends sensitively on the balance between various thermodynamic and kinetic factors related to the high-T-c phase formation and the surface microstructure at the growth front of the deposited film. Under the standard optimized growth conditions for high-quality epitaxial films, the deposition of a YBa2Cu3O7-delta film on an atomically smooth (110) SrTi0(3) substrate, for example, is characterized by a strong damping in the reflection high-energy electron diffraction (RHEED) oscillation suggesting a predominant island growth mode. We have demonstrated that with an atomic oxygen and the technique of RHEED-controlled growth interruption it is possible to minimize surface roughness and to fabricate unit-cell smooth YBa2Cu3O7-delta films over a large area (similar to 0.5 cmX1 cm). The results of this study suggest that two-dimensional layer growth can be induced by the combined use of atomic oxygen and growth conditions, such as low deposition rate, low oxygen partial pressure (<2 mTorr), that produce low supersaturation at the growth front.