Context.The Galactic centre (GC) is of fundamental astrophysical interest, but existing near-infrared surveys fall short covering it adequately, either in terms of angular resolution, multi-wavelength coverage, or both. Here we introduce the GALACTICNUCLEUS survey, aJHK_simaging survey of the centre of the Milky Way with a 0.2″ angular resolution.Aims.The purpose of this paper is to present the observations of Field 1 of our survey, centred approximately on SgrA* with an approximate size of 7.95′ × 3.43′. We describe the observational set-up and data reduction pipeline and discuss the quality of the data. Finally, we present the analysis of the data.Methods.The data were acquired with the near-infrared camera High Acuity Wide field K-band Imager (HAWK-I) at the ESO Very Large Telescope (VLT). Short readout times in combination with the speckle holography algorithm allowed us to produce final images with a stable, Gaussian PSF (point spread function) of 0.2″ FWHM (full width at half maximum). Astrometric calibration is achieved via the VISTA Variables in the Via Lactea (VVV) survey and photometric calibration is based on the SIRIUS/Infrared Survey Facility telescope (IRSF) survey. The quality of the data is assessed by comparison between observations of the same field with different detectors of HAWK-I and at different times.Results.We reach 5σdetection limits of approximatelyJ= 22,H= 21, andK_s= 20. The photometric uncertainties are less than 0.05 atJ≲ 20,H≲ 17, andK_s≲ 16. We can distinguish five stellar populations in the colour-magnitude diagrams; three of them appear to belong to foreground spiral arms, and the other two correspond to high- and low-extinction star groups at the GC. We use our data to analyse the near-infrared extinction curve and find some evidence for a possible difference between the extinction index betweenJ−HandH−K_s. However, we conclude that it can be described very well by a power law with an index ofα_JHKs= 2.30 ± 0.08. We do not find any evidence that this index depends on the position along the line of sight, or on the absolute value of the extinction. We produce extinction maps that show the clumpiness of the ISM (interstellar medium) at the GC. Finally, we estimate that the majority of the stars have solar or super-solar metallicity by comparing our extinction-corrected colour-magnitude diagrams with isochrones with different metallicities and a synthetic stellar model with a constant star formation.