We present the discovery of TOI-1420b, an exceptionally low-density ({rho}=0.08{+/-}0.02g/cm^3^) transiting planet in a P=6.96days orbit around a late G-dwarf star. Using transit observations from TESS, LCOGT, Observatoire Prive du Mont, Whitin, Wendelstein, OAUV, Ca l'Ou, and KeplerCam, along with radial velocity observations from HARPS-N and NEID, we find that the planet has a radius of Rp=11.9{+/-}0.3R{Earth} and a mass of Mp=25.1{+/-}3.8M{Earth}. TOI-1420b is the largest known planet with a mass less than 50M{Earth}, indicating that it contains a sizeable envelope of hydrogen and helium. We determine TOI-1420b's envelope mass fraction to be f~=82_-6_^+7^% , suggesting that runaway gas accretion occurred when its core was at most four to five times the mass of the Earth. TOI-1420b is similar to the planet WASP-107b in mass, radius, density, and orbital period, so a comparison of these two systems may help reveal the origins of close-in low-density planets. With an atmospheric scale height of 1950km, a transmission spectroscopy metric of 580, and a predicted Rossiter-McLaughlin amplitude of about 17m/s, TOI-1420b is an excellent target for future atmospheric and dynamical characterization.