This paper describes a combined computational and experimental study of the noise of exhaust jets with operating conditions typical of high performance military aircraft engines. The numerical simulations use a hybrid RANS/LES approach for the turbulence modeling. Structured multiblock grids with non-matching interfaces are used to enable details of the nozzle geometry to be included. Dual time-stepping is used to advance the solution in time and multigrid and implicit residual smoothing is used to accelerate the convergence of the sub-iterations. The acoustic field is determined by integration over an acoustic data surface based on solutions to the Ffowcs Williams - Hawkings equation. Both the near and far acoustic fields are determined. Baseline nozzles and nozzles with chevrons for noise reduction are simulated. To simulate the effect of the chevrons, without using a body-fitted grid, an immersed boundary method is used. The companion experiments, whose measurements are used to assess the quality of the numerical simulations, are performed in an anechoic jet facility. The facility includes a forward flight stream and uses helium-air mixtures to simulate the effects of jet heating. Flow and noise measurements are described for both baseline and chevron nozzles. Comparisons are made between the numerical predictions and the measurements.