We present Atacama Large Millimeter/submillimeter Array (ALMA) 1.3 mm continuum images of the asteroid 3 Juno obtained with an angular resolution of 0.042 ′′ (60 km at 1.97 AU). The data were obtained over a single 4.4 hr interval, which covers 60% of the 7.2 hr rotation period, approximately centered on local transit. A sequence of ten consecutive images reveals continuous changes in the asteroid's profile and apparent shape, in good agreement with the sky projection of the three-dimensional model of the Database of Asteroid Models from Inversion Techniques. We measure a geometric mean diameter of 259±4 km, in good agreement with past estimates from a variety of techniques and wavelengths. Due to the viewing angle and inclination of the rotational pole, the southern hemisphere dominates all of the images. The median peak brightness temperature is 215±13 K, while the median over the whole surface is 197 ± 15 K. With the unprecedented resolution of ALMA, we find that the brightness temperature varies across the surface with higher values correlated to the subsolar point and afternoon areas, and lower values beyond the evening terminator. The dominance of the subsolar point is accentuated in the final four images, suggesting a reduction in the thermal inertia of the regolith at the corresponding longitudes, which are possibly correlated to the location of the putative large impact crater. These results demonstrate ALMA's potential to resolve thermal emission from the surface of main belt asteroids, and to measure accurately their position, geometric shape, rotational period, and soil characteristics.