Dimorphos is the tiny satellite of the 65803 Didymos binary system discovered in the early 2000s. Dimorphos is the current active target of the Double Asteroid Redirection Test by NASA, and if successful, Dimorphos will become quite famous as being the first asteroid to ever be manipulated by humankind.
A 10 square mile claim would be enough for basic mining operations and local support structure. Hypothetical estimated value in 2022 USD $1 trillion. The number of available claims is limited to 1.
Image Credit: NASA / JPL-Caltech