Monolayer transition-metal dichalcogenides(TMDs) manifest exceptional optical properties related to narrow excitonic resonances. However, these properties have been so far explored only for structures produced by techniques inducing considerable large-scale inhomogeneity. In contrast, techniques which are essentially free from this disadvantage, such as molecular beam epitaxy (MBE), have to date yielded only structures characterized by considerable spectral broadening, which hinders most of the interesting optical effects. Here, we report for the firsttime on the MBE-grown TMD exhibiting narrow and resolved spectral lines of neutral and charged exciton. Moreover, our material exhibits unprecedented high homogeneity of optical properties, with variation of the exciton energy as small as ±0.16 meV over a distance of tens of micrometers. Our recipe for MBE growth is presented for MoSe2 and includes the use of atomically flat hexagonal boron nitride substrate. This recipe opens a possibility of producing TMD heterostructures with optical quality, dimensions, and homogeneity required for optoelectronic applications.