In bowl, combine salt, pepper, garlic and thyme. Rub salt mixture all over duck and pack snugly in ceramic or glass container. Cover and refrigerate for 10 hours.
Remove duck and rinse off salt mixture. Pat dry.
In heavy-bottomed Dutch oven, warm duck fat over medium heat until liquid. Add legs, making sure all are covered with fat. Transfer to preheated 300°F (150°C) oven and cook, uncovered, until legs are tender, about 4 hours.
Carefully remove pot from oven (fat will be very hot). Using slotted spoon and tongs, remove duck from fat and transfer to clean towel to remove excess fat. Serve warm.