We propose a theoretical framework and a dynamical model for the description of the natural optical activity and the Faraday rotation in an individual chiral single-walled carbon nanotube in the highly nonlinear coherent regime. The model is based on a discrete-level representation of the optically active states near the band edge. Chirality is modelled by a system Hamiltonian corresponding to energy-level configurations, specific for each handedness, that are mirror reflections of each other. An axial magnetic field is introduced through the Aharonov–Bohm and Zeeman energy-level shifts.The time evolution of the quantum system following an ultrafast circularly polarised optical excitation is studied using the coherent vector Maxwell pseudospin equations. Giant natural and magneto-optical gyrotropy, exceeding the one of the artificial photonic metamaterials, is numerically demonstrated for a single (5, 4) carbon nanotube and an estimate of the magnitude of the natural and magneto-chiral circular dichroism and specific optical rotatory power is obtained. The model provides a framework for the investigation of chirality and magnetic field dependence of the ultrafast nonlinear optical response of a single carbon nanotube.