The improvement of radiation resistance in nanocomposite materials is investigated by means of classical reactive molecular dynamics simulations. In particular, we study the influence of carbon nanotubes (CNTs) in an Ni matrix on the trapping and possible outgassing of He. When CNTs are defect-free, He atoms diffuse alongside CNT walls and, although there is He accumulation at the metal-CNT interface, no He trespassing of the CNT wall is observed, which is consistent with the lack of permeability of a perfect graphene sheet. However, when vacancies are introduced to mimic radiation-induced defects, He atoms penetrate CNTs, which play the role of nano-chimneys, allowing He atoms to escape the damaged zone and reduce bubble formation in the matrix. Consequently, composites made of CNTs inside metals are likely to display improved radiation resistance, particularly when radiation damage is related to swelling and He-induced embrittlement.