The formation of moiré patterns in crystalline solids can be used to manipulate their electronic properties, which are fundamentally influenced by periodic potential landscapes. In two-dimensional materials, a moiré pattern with a superlattice potential can be formed by vertically stacking two layered materials with a twist and/or a difference in lattice constant. This approach has led to electronic phenomena including the fractal quantum Hall effect1-3, tunable Mott insulators4,5 and unconventional superconductivity6. In addition, theory predicts that notable effects on optical excitations could result from a moiré potential in two-dimensional valley semiconductors7-9, but these signatures have not been detected experimentally. Here we report experimental evidence of interlayer valley excitons trapped in a moiré potential in molybdenum diselenide (MoSe2)/tungsten diselenide (WSe2) heterobilayers. At low temperatures, we observe photoluminescence close to the free interlayer exciton energy but with linewidths over one hundred times narrower (around 100 microelectronvolts). The emitter g-factors are homogeneous across the same sample and take only two values, -15.9 and 6.7, in samples with approximate twist angles of 60 degrees and 0 degrees, respectively. The g-factors match those of the free interlayer exciton, which is determined by one of two possible valley-pairing configurations. At twist angles of approximately 20 degrees the emitters become two orders of magnitude dimmer; however, they possess the same g-factor as the heterobilayer at a twist angle of approximately 60 degrees. This is consistent with the umklapp recombination of interlayer excitons near the commensurate 21.8-degree twist angle7. The emitters exhibit strong circular polarization of the same helicity for a given twist angle, which suggests that the trapping potential retains three-fold rotational symmetry. Together with a characteristic dependence on power and excitation energy, these results suggest that the origin of the observed effects is interlayer excitons trapped in a smooth moiré potential with inherited valley-contrasting physics. This work presents opportunities to control two-dimensional moiré optics through variation of the twist angle.