The paper presents the development of a compact, centimetre-scale accelerator capable of producing high-quality electron beams with energies up to 1 GeV. Traditional radiofrequency-based accelerators require large distances to achieve multi-GeV beam energies, while laser-wakefield accelerators can produce electric fields of 10–100 GV m$^{-1}$, enabling more compact devices. However, previous attempts to achieve GeV energies with laser-wakefield accelerators were limited by the required laser intensity and the energy spread of the electron beams. The authors demonstrate the use of a gas-filled capillary discharge waveguide to guide a 40 TW peak-power laser pulse over a 3.3 cm distance, achieving a 1 GeV electron beam with per-centile level energy spread and low divergence. The capillary waveguide, filled with hydrogen gas, was created using a laser-machined sapphire block and a high-voltage pulser. The laser beam was focused onto the entrance of the capillary using an off-axis parabola, and the guiding efficiency was measured using optical diodes. The performance of the accelerator was optimized by adjusting the initial gas density and the timing between the laser pulse arrival and the onset of the discharge. The electron beam energy was measured using a magnetic spectrometer, and the energy spread and divergence were calculated. The results show that the accelerator can produce electron beams at energies of 0.5 GeV and 1.0 GeV with per-centile level energy spread and low divergence. The paper discusses the challenges and limitations of the accelerator, including the impact of laser pulse evolution, self-focusing, and beam loading on the plasma wake. The authors suggest that controlled particle injection via laser triggering may be necessary to ensure stability at higher energies. The compact nature of the accelerator offers unique applications, such as driving pulsed radiation sources and enabling compact free-electron lasers producing keV X-rays.The paper presents the development of a compact, centimetre-scale accelerator capable of producing high-quality electron beams with energies up to 1 GeV. Traditional radiofrequency-based accelerators require large distances to achieve multi-GeV beam energies, while laser-wakefield accelerators can produce electric fields of 10–100 GV m$^{-1}$, enabling more compact devices. However, previous attempts to achieve GeV energies with laser-wakefield accelerators were limited by the required laser intensity and the energy spread of the electron beams. The authors demonstrate the use of a gas-filled capillary discharge waveguide to guide a 40 TW peak-power laser pulse over a 3.3 cm distance, achieving a 1 GeV electron beam with per-centile level energy spread and low divergence. The capillary waveguide, filled with hydrogen gas, was created using a laser-machined sapphire block and a high-voltage pulser. The laser beam was focused onto the entrance of the capillary using an off-axis parabola, and the guiding efficiency was measured using optical diodes. The performance of the accelerator was optimized by adjusting the initial gas density and the timing between the laser pulse arrival and the onset of the discharge. The electron beam energy was measured using a magnetic spectrometer, and the energy spread and divergence were calculated. The results show that the accelerator can produce electron beams at energies of 0.5 GeV and 1.0 GeV with per-centile level energy spread and low divergence. The paper discusses the challenges and limitations of the accelerator, including the impact of laser pulse evolution, self-focusing, and beam loading on the plasma wake. The authors suggest that controlled particle injection via laser triggering may be necessary to ensure stability at higher energies. The compact nature of the accelerator offers unique applications, such as driving pulsed radiation sources and enabling compact free-electron lasers producing keV X-rays.