Unicorn horns are incredibly powerful magical reagents used in everything from potions to wands. They are not, however, rare.
Several times a year, when the moon hits the right angle, unicorns lose their horns for a few hours as the old ones fall off and new ones grow in. The time of year is different for each creature, though family members tend to shed within a few weeks of each other.
Discarded horns are then gathered up for trade and stored in trees until the next Phantasmaflora, the farmer’s market in the village of Peyroux, or other magic rich markets.