Low-dimensional electron systems, as realized in layered materials, often tend to spontaneously break the symmetry of the underlying nuclear lattice by forming so-called density waves(1); a state of matter that at present attracts enormous attention(2-6). Here we reveal a remarkable and surprising feature of charge density waves, namely their intimate relation to orbital order. For the prototypical material 1T-TaS2 we not only show that the charge density wave within the two-dimensional TaS2 layers involves previously unidentified orbital textures of great complexity. We also demonstrate that two metastable stackings of the orbitally ordered layers allow manipulation of salient features of the electronic structure. Indeed, these orbital effects provide a route to switch 1T-TaS2 nanostructures from metallic to semiconducting with technologically pertinent gaps of the order of 200meV. This new type of orbitronics is especially relevant for the ongoing development of novel, miniaturized and ultrafast devices based on layered transition metal dichalcogenides(7,8).