About 1 out of 200 Sun-like stars has a planet with an orbital period shorter than one day: an ultrashort-period planet(1,2). All of the previously known ultrashort-period planets are either hot Jupiters, with sizes above 10 Earth radii (R-circle plus), or apparently rocky planets smaller than 2 R-circle plus. Such lack of planets of intermediate size (the `hot Neptune desert') has been interpreted as the inability of low-mass planets to retain any hydrogen/ helium (H/He) envelope in the face of strong stellar irradiation. Here we report the discovery of an ultrashort-period planet with a radius of 4.6 R-circle plus and a mass of 29 M-circle plus, firmly in the hot Neptune desert. Data from the Transiting Exoplanet Survey Satellite(3) revealed transits of the bright Sun-like star LTT 9779 every 0.79 days. The planet's mean density is similar to that of Neptune, and according to thermal evolution models, it has a H/He-rich envelope constituting 9.0(-2.9)(+2.7) % of the total mass. With an equilibrium temperature around 2,000 K, it is unclear how this `ultrahot Neptune' managed to retain such an envelope. Follow-up observations of the planet's atmosphere to better understand its origin and physical nature will be facilitated by the star's brightness (V-mag = 9.8).