Working in batches, add chicken to the skillet in a single layer and cook until golden brown and cooked through, reaching an internal temperature of 165 degrees F, about 4-5 minutes per side; set aside.
Season chicken with 3/4 teaspoon salt and 1/2 teaspoon pepper. Melt 2 tablespoons butter in a large skillet over medium heat.
Melt remaining 3 tablespoons butter. Add shallot, and cook, stirring frequently, until tender, about 3-5 minutes. Stir in garlic and thyme until fragrant, about 1 minute.