How to Make It
Preheat the oven to 375°. In a medium roasting pan, toss the potatoes with 2 tablespoons of the olive oil. Season with salt and pepper and roast for about 25 minutes, until golden and tender.
Meanwhile, in a small saucepan, boil the stock until reduced to 1/2 cup, 8 to 10 minutes. Remove from the heat and add the butter and truffle oil; keep warm.
In a large nonstick skillet, heat 1 tablespoon of the olive oil until shimmering. Season the chicken breasts with salt and pepper and add them to the skillet, skin side down. Cook over moderately high heat, turning once, until browned and cooked through, about 16 minutes. Transfer the chicken breasts to plates and keep warm. Wipe out the skillet.
Add the remaining 3 tablespoons of olive oil to the skillet. Crack the eggs into the skillet and cook over moderate heat until the whites are set, about 1 1/2 minutes. Flip the eggs and cook for 20 seconds longer. Using a spatula, transfer the eggs and the potatoes to the chicken. Drizzle with the truffle sauce and serve.