The carriers of the diffuse interstellar bands (DIBs) are largely unidentified molecules ubiquitously present in the interstellar medium (ISM). After decades of study, two strong and possibly three weak near-infrared DIBs have recently been attributed to the C^+^_60_ fullerene based on observational and laboratory measurements. There is great promise for the identification of the over 400 other known DIBs, as this result could provide chemical hints towards other possible carriers. In an effort to systematically study the properties of the DIB carriers, we have initiated a new large-scale observational survey: the ESO Diffuse Interstellar Bands Large Exploration Survey (EDIBLES). The main objective is to build on and extend existing DIB surveys to make a major step forward in characterising the physical and chemical conditions for a statistically significant sample of interstellar lines-of-sight, with the goal to reverse-engineer key molecular properties of the DIB carriers. EDIBLES is a filler Large Programme using the Ultraviolet and Visual Echelle Spectrograph at the Very Large Telescope at Paranal, Chile. It is designed to provide an observationally unbiased view of the presence and behaviour of the DIBs towards early-spectral-type stars whose lines-of-sight probe the diffuse-to-translucent ISM. Such a complete dataset will provide a deep census of the atomic and molecular content, physical conditions, chemical abundances and elemental depletion levels for each sightline. Achieving these goals requires a homogeneous set of high-quality data in terms of resolution (R~70000-100000), sensitivity (S/N up to 1000 per resolution element), and spectral coverage (305-1042nm), as well as a large sample size (100+ sightlines). In this first paper the goals, objectives and methodology of the EDIBLES programme are described and an initial assessment of the data is provided.