The motion of CH3NH3+ cations in the low-temperature phase of the promising photovoltaic material methylammonium lead triiodide (CH3NH3PbI3) is investigated experimentally as well as theoretically, with a particular focus on the activation energy. Inelastic and quasi-elastic neutron scattering measurements reveal an activation energy of ∼48 meV. Through a combination of experiments and first-principles calculations, we attribute this activation energy to the relative rotation of CH3 against an NH3 group that stays bound to the inorganic cage. The inclusion of nuclear quantum effects through path integral molecular dynamics gives an activation energy of ∼42 meV, in good agreement with the neutron scattering experiments. For deuterated samples (CD3NH3PbI3), both theory and experiment observe a higher activation energy for the rotation of CD3 against NH3, which results from the smaller nuclear quantum effects in CD3. The rotation of the NH3 group, which is bound to the inorganic cage via strong hydrogen bonding, is unlikely to occur at low temperatures due to its high energy barrier of ∼120 meV.