We demonstrate direct epitaxial growth of high-quality hexagonal boron nitride (hBN) layers on graphite using high-temperature plasma-assisted molecular beam epitaxy. Atomic force microscopy reveals mono- and few-layer island growth, while conducting atomic force microscopy shows that the grown hBN has a resistance which increases exponentially with the number of layers, and has electrical properties comparable to exfoliated hBN. X-ray photoelectron spectroscopy, Raman microscopy and spectroscopic ellipsometry measurements on hBN confirm the formation of sp2-bonded hBN and a band gap of 5.9 ± 0.1 eV with no chemical intermixing with graphite. We also observe hexagonal moiré patterns with a period of 15 nm, consistent with the alignment of the hBN lattice and the graphite substrate.