Epilayers of GaN were grown on patterned Si (111) substrates of various terrace widths by means of metal organic chemical vapor deposition. The technique of lateral epitaxy on a patterned substrate used the growth of GaN epilayers from the periodic and parallel stripes that form as a result of the substrate etching. Silicon substrates were patterned for various terrace widths of 3 μm, 8 μm, and 18 μm. A low temperature AIN was used as a seed layer for the growth of a 1.5 μm thick GaN epilayer. The as-grown samples were characterized by using double-crystal X-ray diffractometry (DCXRD), photoluminescence and atomic force microscopy (AFM). From the DCXRD spectra, the full width at half maximum (FWHM) of the samples was found to decrease as the terrace width decreased. This behavior indicates that there is an improvement in the crystalline quality of the GaN epilayers as the terrace width decreases. The photoluminescence spectra reveal a decrease in the FWHM and an increase in the peak intensity as the terrace width decreases. This behavior indicates that there is an improvement in the optical quality of the GaN epilayer as the terrace width decreases. The atomic force micrographs reveal a dislocation-free homogeneous surface in the trench region compared to the terrace region with defects such as pits and dislocations. The results clearly show that GaN epilayers grown on a patterned Si substrate with a terrace width 3 μm have a good crystalline quality with minimal threading dislocation and excellent band edge emission.