Hexagonal boron nitride (h-BN), a layered material similar to graphite, is a promising dielectric. Monolayer h-BN, so-called "white graphene", has been isolated from bulk BN and could be useful as a complementary two-dimensional dielectric substrate for graphene electronics. Here we report the large area synthesis of h-BN films consisting of two to five atomic layers, using chemical vapor deposition. These atomic films show a large optical energy band gap of 5.5 eV and are highly transparent over a broad wavelength range. The mechanical properties of the h-BN films, measured by nanoindentation, show 2D elastic modulus in the range of 200-500 N/m, which is corroborated by corresponding theoretical calculations.