The Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE) is a blind narrow-band (NB) Hα+[NII] imaging survey carried out with MegaCam at the Canada-France-Hawaii Telescope. The survey covers the whole Virgo cluster region from its core to one virial radius (104 deg2). The sensitivity of the survey is of f(Hα) ∼ 4 × 10-17 erg s-1 cm-2 (5σ detection limit) for point sources and Σ(Hα) ∼ 2 × 10-18 erg s-1 cm-2 arcsec-2 (1σ detection limit at 3 arcsec resolution) for extended sources, making VESTIGE the deepest and largest blind NB survey of a nearby cluster. This paper presents the survey in all its technical aspects, including the survey design, the observing strategy, the achieved sensitivity in both the NB Hα+[NII] and in the broad-band r filter used for the stellar continuum subtraction, the data reduction, calibration, and products, as well as its status after the first observing semester. We briefly describe the Hα properties of galaxies located in a 4 × 1 deg2 strip in the core of the cluster north of M87, where several extended tails of ionised gas are detected. This paper also lists the main scientific motivations for VESTIGE, which include the study of the effects of the environment on galaxy evolution, the fate of the stripped gas in cluster objects, the star formation process in nearby galaxies of different type and stellar mass, the determination of the Hα luminosity function and of the Hα scaling relations down to ∼106 M⊙ stellar mass objects, and the reconstruction of the dynamical structure of the Virgo cluster. This unique set of data will also be used to study the HII luminosity function in hundreds of galaxies, the diffuse Hα+[NII] emission of the Milky Way at high Galactic latitude, and the properties of emission line galaxies at high redshift.