Two-dimensional (2D) materials(1-5) offer a unique platform from which to explore the physics of topology and many-body phenomena. New properties can be generated by filling the van der Waals gap of 2D materials with intercalants(6,7); however, post-growth intercalation has usually been limited to alkali metals(8-10). Here we show that the self-intercalation of native atoms(11,12) into bilayer transition metal dichalcogenides during growth generates a class of ultrathin, covalently bonded materials, which we name ic-2D. The stoichiometry of these materials is defined by periodic occupancy patterns of the octahedral vacancy sites in the van der Waals gap, and their properties can be tuned by varying the coverage and the spatial arrangement of the filled sites(7,13). By performing growth under high metal chemical potential(14,15) we can access a range of tantalum-intercalated TaS(Se)(y), including 25% Ta-intercalated Ta9S16, 33.3% Ta-intercalated Ta7S12, 50% Ta-intercalated Ta10S16, 66.7% Ta-intercalated Ta8Se12 (which forms a Kagome lattice) and 100% Ta-intercalated Ta9Se12. Ferromagnetic order was detected in some of these intercalated phases. We also demonstrate that self-intercalated V11S16, In11Se16 and FexTey can be grown under metal-rich conditions. Our work establishes self-intercalation as an approach through which to grow a new class of 2D materials with stoichiometry- or composition-dependent properties.