Fibre-optic components fabricated on the same substrate as integrated circuits are important for future high-speed communications. One industry response has been the costly push to develop indium phosphide (InP) electronics. However, for fabrication simplicity, reliability and cost, gallium arsenide (GaAs) remains the established technology for integrated optoelectronics. Unfortunately, the GaAs bandgap wavelength (0.85 mum) is far too short for fibre optics at 1.3-1.5 mum. This has led to work on materials that have a large lattice mismatch on GaAs. Here we demonstrate the first light-emitting diode (LED) that emits at 1.5 mum fibre-optic wavelengths in GaAs using optical transitions from arsenic antisite (AsGa) deep levels. This is an enabling technology for fibre-optic components that are lattice-matched to GaAs integrated circuits. We present experimental results showing significant internal optical power (24 mW) and speed (in terahertz) from GaAs optical emitters using deep-level transitions. Finally, we present theory showing the ultimate limit to the efficiency-bandwidth product of semiconductor deep-level optical emitters.