We present the first entirely ground-based astrometric determination of the proper motion for the Fornax Local Group dwarf spheroidal satellite galaxy of the Milky Way (MW), using charge-coupled device data acquired with the ESO 3.5 m New Technology Telescope at La Silla Observatory in Chile. Our unweighted mean from five quasar fields in the background of Fornax, used as fiducial reference points, leads to μαcos δ = 0.62 ± 0.16 mas yr-1 and μδ = -0.53 ± 0.15 mas yr-1. A detailed comparison with all previous measurements of this quantity seems to imply that there is still no convincing convergence to a single value, perhaps indicating the existence of unaccounted systematic effects in (some of) these measurements. From all available proper-motion and radial velocity measurements for Fornax, we compute Fornax's orbital parameters and their uncertainty using a realistic Galactic potential and a Monte Carlo simulation. Properties of the derived orbits are then compared to main star formation episodes in the history of Fornax. All published proper-motion values imply that Fornax has recently (200-300 Myr ago) approached perigalacticon at a distance of ~150 kpc. However, the derived period exhibits a large scatter, as does the apogalacticon. Our orbit, being the most energetic, implies a very large apogalactic distance of ~950 kpc. If this were the case, then Fornax would be a representative of a hypervelocity MW satellite in late infall. Based on observations made with ESO Telescopes at the La Silla Observatory under programme. IDs lang060.A-9701rang, lang065.N-0472rang, lang0.66.B-0276rang, lang074.B-0456rang, lang076.B-0528rang, lang079.B-0379rang, lang080.B-0144rang, lang081.B-0534rang, and lang082.B-0034rang.