Large eddy simulations (LES) are performed for a heated over-expanded supersonic turbulent jet issued from a converging-diverging round nozzle with chevrons. The unsteady flow processes and shock/turbulence interactions are investigated with the unstructured LES framework developed at Cascade Technologies. In this study, the complex geometry of the nozzle and chevrons (12 counts, 6° penetration) are explicitly included in the computational domain using unstructured body-fitted mesh and adaptive grid refinement. Sound radiation from the jet is computed using an efficient frequency-domain implementation of the Ffowcs Williams-Hawkings equation. Noise predictions are compared to experimental measurements carried out at the United Technologies Research Center for the same nozzle and operating conditions. The initial blind comparisons show good agreement in terms of spectra shape and levels for both the near-field and far-field noise. Additional analysis of the large database generated by the LES is ongoing. Preliminary results show that the current simulation captures the main flow and noise features, including the shock cells, broadband shock-associated noise and turbulent mixing noise.