Fully unstructured large-eddy simulation coupled with a Ffowcs Williams-Hawkings solver was used to predict the noise from underexpanded supersonic jets issuing from rectangular nozzles. The effect of the chevrons was considered by comparing simulations with and without the addition of chevrons around the nozzle lip. The entire flow in and around the nozzle is simulated using the CharLES solver, on unstructured meshes containing up to 528 million control volumes. The massively parallel code was scaled up to as many as 163,840 processors. A mesh sensitivity study was performed, and the far-field noise predictions were compared with measurements conducted at the NASA Glenn Research Center. For the underexpanded isothermal operating conditions considered, chevrons are observed to produce a substantial noise reduction.