Ga0.5In0.5P is observed to form the CuPt ordered structure during organometallic vapor phase epitaxy (OMVPE). Of the four possible {111} planes on which CuPt ordering could occur, only two are observed for growth on (001)-oriented substrates, giving the (1BAR11) and (1BAR11) variants. The mechanism by which ordering occurs is not completely understood. Recent total energy calculations indicate that the phenomenon can be explained on the basis of thermodynamic considerations. Indirect evidence indicates that kinetic factors, including processes occurring at steps propagating across the surface in the two-dimensional growth mode, affect ordering. In this letter, Ga0.5In0.5P layers have been grown on (001)GaAs substrates by OMVPE. In order to examine the effects of surface kinetic factors, the substrates were first patterned with [110] oriented grooves 5-mu-m wide and from 0.2 to 1-mu-m deep. This yields adjacent areas of epitaxial material within the grooves produced by growth via the motion of steps in opposite directions. Transmission electron diffraction reveals that the two directions of step motion produce two different variants. For exactly (001) oriented substrates, one half of the groove is filled with a single domain of the (1BAR11) variant while the other half is also a single domain, but of the (11BAR1) variant. For substrates misoriented by 6-degrees to give [110] steps, the domains are asymmetric. The domains are very large, several square microns in cross section extending along the entire length of the groove. The strong intensities of the order-induced spots indicate a high degree of order in the material grown in the grooves. These results demonstrate directly, for the first time, that kinetic factors related to the motion of steps on the surface determine the ordered structure formed. They also demonstrate the possibility of producing very large domains of ordered material.