1. Preheat the oven to 180 degrees Celsius, pat the skin of the chicken dry with a paper towel and season the chicken.
2. In an ovenproof frying pan melt half of the butter over a medium heat. Add the chicken, skin side down and cook it for about 5 minutes or until it is golden brown, turn it and cook for a further 2 minutes. Place the chicken onto a plate and then add the potatoes to the pan. Cook, turning them regularly for about 4-5 minutes or until they are golden and then put them onto a plate. Add the 4 lemon halves cut side down to the pan and cook them for about 2 minutes until they are caramelised and then place them onto a plate.
3. Reduce the heat to low and squeeze the juice from the remaining lemon halves into the pan, stir to deglaze. Add the squeezed lemon halves, potatoes, oregano, and garlic to the pan and cook for about 2 minutes. Remove this from the heat and add the stock. Arrange the chicken, skin side up on top of the potatoes and bake in the preheated oven for 25-30 minutes or until the chicken is cooked through and the potatoes are tender. Place the chicken, potatoes, and garlic onto a plate and cover to keep them warm.
4. Strain the liquid from the pan into a small saucepan and discard the solids. Bring this to the boil over a high heat and cook for about 10-15 minutes until the sauce reduces and thickens slightly. Stir in the rest of the butter until it melts, season and then drizzle the sauce over the chicken and the potatoes.