Hexagonal boron nitride (h-BN) is a tantalizing material for solid-state quantum engineering. Analogously to three-dimensional wide-bandgap semiconductors like diamond, h-BN hosts isolated defects exhibiting visible fluorescence, and the ability to position such quantum emitters within a two-dimensional material promises breakthrough advances in quantum sensing, photonics, and other quantum technologies. Critical to such applications, however, is an understanding of the physics underlying h-BN's quantum emission. We report the creation and characterization of visible single-photon sources in suspended, single-crystal, h-BN films. The emitters are bright and stable over timescales of several months in ambient conditions. With substrate interactions eliminated, we study the spectral, temporal, and spatial characteristics of the defects' optical emission, which offer several clues about their electronic and chemical structure. Analysis of the defects' spectra reveals similarities in vibronic coupling despite widely-varying fluorescence wavelengths, and a statistical analysis of their polarized emission patterns indicates a correlation between the optical dipole orientations of some defects and the primitive crystallographic axes of the single-crystal h-BN film. These measurements constrain possible defect models, and, moreover, suggest that several classes of emitters can exist simultaneously in free-standing h-BN, whether they be different defects, different charge states of the same defect, or the result of strong local perturbations.Defect engineering in solid-state materials is a rapidly progressing field with applications in quantum information science [1, 2], nanophotonics [3], and nanoscale sensing in biology and chemistry [4]. Inspired by the success of the archetypal nitrogen-vacancy center in diamond [5], recent efforts have uncovered analogous systems in other wide-bandgap semiconductors such as silicon carbide [6, 7] which offer exciting new opportunities for defect engineering in three-dimensional materials. However, optically active impurities in low-dimensional materials and thin films can provide unique functionalities due to intrinsic spatial confinement and the ability to create multi-functional layered materials [8, 9]. Within the class of van der Waals materials, hexagonal boron nitride (h-BN) is an ideal candidate for exploring new defect physics due to its large (∼6 eV) bandgap [10] and its unique optical [11], electrical [12, 13], and vibronic properties [14] that may influence the underlying physics of its defects. At present, however, progress is impeded by an incomplete understanding of the electronic and chemical structure of defects responsible for h-BN's visible fluorescence.