This paper investigates numerically the acoustic sources and far-field noise of chevron and round jets. The acoustic sources are described by the fourth-order space–time velocity cross correlations, which are calculated based on a large-eddy simulation flowfield. Gaussian functions are found to fit the axial, radial, and azimuthal cross correlations reasonably well. The axial length scales are three to four times the radial and azimuthal length scales. For the chevron jet, the cross-correlation scales vary with azimuthal angle up to six jet diameters downstream; beyond that, they become axisymmetric like those for a round jet. The fourth-order space–time cross correlation of the axial velocity R_1111 is the dominant source component, and there are considerable contributions from other source components such as R_2222, R_3333, R_1212, R_1313, and R_2323 cross correlations where 1, 2, and 3 represent axial, radial, and azimuthal directions, respectively. For the chevron jet, these cross correlations decay rapidly with axial distance whereas for the round jet, they remain roughly constant over the first 10 jet diameters. The chevron jet intensifies both the R_2222 and R_3333 cross correlations within two jet diameters of the jet exit. The amplitude, length, and time scales of the cross-correlations of a large-eddy simulation velocity field are investigated as functions of position and are found to be proportional to the turbulence amplitude, length, and time scales that are determined from a Reynolds-averaged Navier–Stokes calculation. The constants of proportionality are found to be independent of position within the jet, and they are quite close for chevron and round jets. The scales derived from Reynolds-averaged Navier–Stokes are used for source description, and an acoustic analogy is used for sound propagation. There is an excellent agreement between the far-field noise predictions and measurements. At low frequencies, the chevron nozzle significantly reduces the far-field noise by 5–6 dB at 30 deg and 2–3 dB at 90 deg to the jet axis. However, the chevron nozzle slightly increases high-frequency noise. It was found that R_1212 and R_1313 cross correlations have the largest contribution to the jet noise at 30 deg to the jet axis, whereas the R_2323 cross correlation has the largest contribution to the jet noise at 90 deg to the jet axis. The Reynolds-averaged Navier–Stokes calculations are repeated with different turbulence models, and the noise prediction is found to be almost insensitive to the turbulence model. The results indicate that the modeling approach is capable of assessing advanced noise-reduction concepts.