The concept of chiral tunneling in metallic single-wall carbon nanotubes, originating from the interplay of local electrostatic and pseudomagnetic potentials, is considered and applied to an evaluation of the Josephson current in a nanotube-based superconductor--normal metal--superconductor (SNS) junction and the persistent current in a circular nanotube. In the former case, an oscillatory dependence of the critical supercurrent on the potential strength and the nanotube chiral angle is predicted. In the latter case, the existence of a spontaneous persistent current in an isolated ringlike nanotube is discussed.