We report the discovery of the largest giant radio galaxy yet, J1420-0545: a FR type II radio source with an angular size of 17.4', identified with an optical galaxy at z = 0.3067. Thus, the projected linear size of the radio structure is 4.69 Mpc (if we assume that H0 = 71 km s-1 Mpc-1, Ωm = 0.27, and ΩΛ = 0.73). This makes it larger than 3C 236, which is the largest double radio source known to date. New radio observations with the 100 m Effelsberg telescope and the Giant Metrewave Radio Telescope, as well as optical identification with a host galaxy and its optical spectroscopy with the William Herschel Telescope, are reported. The spectrum of J1420-0545 is typical of elliptical galaxies in which continuum emission with the characteristic 4000 Å discontinuity and the H and K absorption lines are dominated by evolved stars. The dynamical age of the source, its jets' power, the energy density, and the equipartition magnetic field are calculated and compared with the corresponding parameters of other giant and normal-sized radio galaxies from a comparison sample. The source is characterized by the exceptionally low density of the surrounding IGM and an unexpectedly high expansion speed of the source along the jet axis. All of these may suggest a large inhomogeneity of the IGM.