This castle on a hill overlooking an important crossroads (trivium in Latin, hence Trebbio) in the Val di Sieve near San Piero a Sieve belonged to the founder of the Medici bank, Giovanni di Bicci de' Medici.
After Giovanni di Bicci's death in 1429, his son Cosimo hired Michelozzo to remodel it in fortified villa with a tower, making the second Medici villa (after the nearby Cafaggiolo) to get a Michelozzo overhaul. Grand Duke Cosimo frequently used it as a hunting lodge, and in 1644 Ferdinando II sold it, and it's privately owned to this day.
Image by Sailko, GNU Free Documentation License