Preheat the oven to 180C/350F.
Salt and pepper chicken thighs and brown them over high heat in a frying pan in batches to avoid overcrowding and steaming until golden on both sides. ( You can skip oil if using non-stick frying pan.) Remove to a plate and set aside. Discard all oil but 1-2 tbsp.
To the same pan add anchovies, sliced garlic and half the rosemary, fry over medium heat while stirring and trying to break up anchovies into a paste for 1 minute.
Add tomato passata, water, olives, beans and bring to a boil. Taste the sauce and add salt if needed but be careful as both anchovies and olives are salty.
Return the chicken back to the pan together with the juices that collected at the bottom of the plate and remaining rosemary. Cover with a lid and cook in the preheated oven for 20 minutes. Then uncover and cook for 20 minutes longer.
Serve with rice, pasta or a green salad for a low-carb option.