We demonstrate selective growth of high-quality GaN by gas-source molecular beam epitaxy on Si(111) wafers patterned with SiO2. GaN was grown on wafers having two different buffer layers. The first buffer layer contains two AlGaN/GaN superlattices, separated by GaN spacer, grown on AlN, with a total thickness of 400 nm. The second is a thin AlN (1.5 nm) buffer layer. X-ray-diffraction confirms (0001) growth orientation, smooth interfaces, and coherence lengths comparable to the layer thickness in both samples. In the case of the thin AlN buffer layer, the tensile stress measured by the E2 Raman line shift is attributed to the mismatch in the thermal expansion coefficients of GaN and Si. However, when the AlGaN/GaN superlattice buffer layer is grown first, a reduced stress is measured. High carrier concentrations (≈1018cm-3) are seen in the GaN grown on the thin AlN buffer layer, which we attribute to the incorporation of silicon from the substrate during the growth process. The superlattice buffer layer is seen to inhibit this diffusion, resulting in a carrier concentration of <1017 cm-3 in the GaN.