A 20 m space telescope is described with an unvignetted 1° field of view—a hundred times larger in area than fields of existing space telescopes. Its diffraction-limited images are a hundred times sharper than from wide-field ground-based telescopes and extend over much if not all the field, 40 arcmin diameter at 500 nm wavelength, for example. The optical system yielding a 1°, 1.36 m diameter image at f/3.9 has relatively small central obscuration, 9% by area on axis, and is fully baffled. Several carousel-mounted instruments can each access directly the full image. The initial instrument complement includes a 400 gigapixel silicon imager with 2 µm pixels (0.005 arcsec), and a 60 gigapixel HgCdTe imager with 5 µm pixels (0.012 arcsec). A multi-object spectrograph with 10 000 fibres will allow spectroscopy with 0.02 arcsec resolution. Direct imaging and spectroscopy of exoplanets can take advantage of the un-aberrated, on-axis image (5 nm RMS wavefront error). While this telescope could be built for operation in free space, a site accessible to a human outpost at the Moon's south pole would be advantageous, for assembly and repairs. The lunar site would allow also for the installation of new instruments to keep up with evolving scientific priorities and advancing technology. Cooling to less than 100E K would be achieved with a surrounding cylindrical thermal shield. This article is part of a discussion meeting issue ‘Astronomy from the Moon: the next decades (part 1)’.