Preheat the oven to 425°F (220°C). Pat the chicken dry and season with salt and pepper.
Heat 1 tablespoon of the olive oil in a large, high-sided ovenproof skillet over medium-high heat. Add the chicken and cook for 4 minutes, until golden. Turn and cook for 2 minutes more, then transfer to a plate.
Reduce the heat to medium. Add the butter and swirl until melted. Add the garlic and cook for 1 minute. Stir in the lemon juice, then remove the skillet from the heat. Pour the butter mixture into a heatproof bowl; stir in the thyme leaves, rosemary, and oregano, and season with salt and pepper.
Add the potatoes and remaining 2 tablespoons olive oil to the skillet. Season with salt and pepper and toss to coat. Roast for 30 minutes, stirring halfway through, until lightly golden.
Stir the potatoes, then arrange the lemon slices, thyme sprigs, and chicken on top. Return to the oven and roast for about 15 minutes, until the chicken reaches 165°F (74°C) and the potatoes are tender.
Drizzle the lemon-herb butter sauce over the chicken and potatoes and garnish with parsley.
Notes
Small potatoes may be replaced with larger potatoes cut into roughly 1-inch pieces.