Kerr frequency combs are well suited for high-capacity data transmission with phase-sensitive modulation formats. This work demonstrates error-free transmission with data rates of up to 1.44 Tbit s−1, spectral efficiencies of up to 6 bit s−1 Hz−1 and transmission distances of up to 300 km. Optical frequency combs have the potential to revolutionize terabit communications1. The generation of Kerr combs in nonlinear microresonators2 is particularly promising3, enabling line spacings of tens of gigahertz. However, such combs may exhibit strong phase noise4,5,6, which has made high-speed data transmission impossible up to now. Here, we demonstrate that systematic adjustment of the pump conditions for low phase noise4,7,8,9 enables coherent data transmission with advanced modulation formats that pose stringent requirements on the spectral purity of the comb. In a first experiment, we encode a data stream of 392 Gbit s−1 on a Kerr comb using quadrature phase-shift keying and 16-state quadrature amplitude modulation. A second experiment demonstrates feedback stabilization of the comb and transmission of a 1.44 Tbit s–1 data stream over up to 300 km. The results show that Kerr combs meet the highly demanding requirements of coherent communications and thus offer an attractive route towards chip-scale terabit-per-second transceivers.