The recently announced Oort-cloud comet C/2014 UN271 (Bernardinelli-Bernstein) is remarkable in at least three respects: (i) it was discovered inbound as far as ~29 au from the Sun (with prediscovery images up to ~34 au); (ii) it showed cometary activity already at almost 24 au; and (iii) its nuclear magnitude (Hr ~ 8.0) indicates an exceptionally large object. Detection of gases is expected in the upcoming years as the comet is heading towards a ~11 au perihelion in 2031. We used ALMA in extended configuration (resolution ~0.064") to measure the 1287 um (233 GHz) continuum flux of the comet. Observations were performed on August 8, 2021 at a 20.0 au distance from the Sun. The high spatial resolution was chosen in order to filter out any dust contribution. We detected the thermal emission of the object at ~10 sigma, with a flux of 0.128+/-0.012 mJy. Based on observational constraints and our theoretical estimates of the dust contribution, the entirety of the measured flux can be attributed to the nucleus. From NEATM modelling combined with the Hr magnitude, we determine a surface-equivalent diameter of 137+/-17 km and a red geometric albedo of 5.3+/-1.2 %. This confirms that 2014 UN271 is by far the largest Oort-cloud object ever found (almost twice as large as comet C/1995 O1 Hale-Bopp), and except for the Centaur 95P/Chiron which shows outburst-like activity, the largest known comet in the Solar System. On the other hand, the object albedo is typical of comets, adding credence for a "universal" comet nucleus albedo. With its distant perihelion and uniquely large size, 2014 UN271 is the prominent archetype of distant comets, whose activity is driven by hypervolatiles. Post-perihelion thermal measurements will permit to study possible albedo changes, such as a surface brightening compared to pre-perihelion, as was observed for Hale-Bopp.