Molecular beam epitaxy was used for the first time to grow novel GaAs/GaSb heterostructures with ultrathin (0.8-3 monolayers) GaAs layers embedded in GaSb. These structures were studied by X-ray diffraction, transmission electron microscopy, and photoluminescence. By contrast to known structures with self-assembled quantum dots, GaAs layers in GaAs/GaSb structures are subject to elastic tensile stresses due to 7% lattice mismatch. The structures exhibit intense photoluminescence in the 2 μm region at low temperatures. Quantum-dimensional islands are formed in the structure at a nominal GaAs layer thickness exceeding 1.5 monolayers. The band alignment of the structures is of type II.