Axisymmetric magnetic string-like objects of nanometre sizes (chiral vortices or skyrmions) have been predicted to exist in a large group of noncentrosymmetric crystals more than two decades ago. Recently, these magnetic textures have been directly observed in nanolayers of cubic helimagnets and monolayers of magnetic metals. We develop a micromagnetic theory of chiral skyrmions in thin magnetic layers for magnetic materials with intrinsic and induced chirality. Such particle-like and stable micromagnetic objects can exist in broad ranges of applied magnetic fields including zero field. Chiral skyrmions can be used as a new type of highly mobile nanoscale data carriers.