Micro-combs [1-4] - optical frequency combs generated by integrated micro-cavity resonators – offer the full potential of their bulk counterparts [5,6], but in an integrated footprint. The discovery of temporal soliton states (DKS – dissipative Kerr solitons) [4,7-11] as a means of mode-locking micro-combs has enabled breakthroughs in many fields including spectroscopy [12,13], microwave photonics [14], frequency synthesis [15], optical ranging [16,17], quantum sources [18,19], metrology [20,21] and more. One of their most promising applications has been optical fibre communications where they have enabled massively parallel ultrahigh capacity multiplexed data transmission [22,23]. Here, by using a new and powerful class of micro-comb called “soliton crystals” [11], we achieve unprecedented data transmission over standard optical fibre using a single integrated chip source. We demonstrate a line rate of 44.2 Terabits per second (Tb/s) using the telecommunications C-band at 1550nm with a spectral efficiency – a critically important performance metric - of 10.4 bits/s/Hz. Soliton crystals exhibit robust and stable generation and operation as well as a high intrinsic efficiency that, together with a low soliton micro-comb spacing of 48.9 GHz enable the use of a very high coherent data modulation format of 64 QAM (quadrature amplitude modulated). We demonstrate error free transmission over 75 km of standard optical fibre in the laboratory as well as in a field trial over an installed metropolitan optical fibre network. These experiments were greatly aided by the ability of the soliton crystals to operate without stabilization or feedback control. This work demonstrates the capability of optical soliton crystal micro-combs to perform in demanding and practical optical communications networks.