Realization of graphene devices is often hindered by the fact that the known layer growth methods do not meet the requirements of the device fabrication in silicon mainstream technology. For example, the relatively straightforward method of decomposition of hexagonal SiC is not CMOS-compatible due to the high-thermal budget it requires [Moon et al., IEEE Electron Device Lett. 31, 260 (2010)]. Techniques based on layer transfer are restricted because of the uncertainty of residual metal contaminants, particles, and structural defects. Of interest is thus a method that would allow one to grow a graphene film directly in the device area where graphene is needed. Production of large area graphene is not necessarily required in this case, but high quality of the film and metal-free growth on an insulating substrate at temperatures below 1000 °C are important requirements. We demonstrate direct growth of defect-free graphene on insulators at moderate temperatures by molecular beam epitaxy. The quality of the graphene was probed by high-resolution Raman spectroscopy, indicating a negligible density of defects. The spectra are compared with those from graphene flakes mechanically exfoliated from native graphite onto mica. These results are combined with insights from density functional theory calculations. A model of graphene growth on mica and similar substrates is proposed.