Aims. We perform a deep search for galaxies in the redshift range 6.5 <= z <= 7.5, to measure the evolution of the number density of luminous galaxies in this redshift range and derive useful constraints on the evolution of their luminosity function. Methods. We present here the first results of an ESO Large Programme, which exploits the unique combination of area and sensitivity provided in the near-IR by the camera Hawk-I at the VLT. We have obtained two Hawk-I pointings on the GOODS South field for a total of similar to 32 observing hours, covering similar to 90 arcmin(2). The images reach Y = 26.7 mag for the two fields. We used public ACS images in the z band to select z-dropout galaxies with the colour criteria Z - Y >= 1, Y - J < 1.5, and Y - K < 2. The other public data in the UBVRIJK bands are used to reject possible low redshift interlopers. The output has been compared with extensive Monte Carlo simulations to quantify the observational effects of our selection criteria, as well as the effects of photometric errors. Results. We detect 7 high-quality candidates in the magnitude range Y = 25.5-26.7. This interval samples the critical range for M(*) at z > 6 (M(1500) similar or equal to -19.5 to -21.5). After accounting for the expected incompleteness, we rule out a luminosity function constant from z = 6 to z = 7 at a 99% confidence level, even including the effects of cosmic variance. For galaxies brighter than M(1500) = -19.0, we derive a luminosity density rho(UV) = 1.5(-0.9)(+2.0) x 10(25) erg s(-1) Hz(-1) Mpc(-3), implying a decrease by a factor 3.5 from z = 6 to z similar or equal to 6.8. On the basis of our findings, we make predictions for the surface densities expected in future surveys, based on ULTRA-VISTA, HST-WFC3, or JWST-NIRCam, evaluating the best observational strategy to maximise their impact.