Heat a large skillet or pot (cast-iron preferred) over medium-high heat. Place the chicken thighs and sauté until lightly golden brown, about 3 minutes per side. Transfer the chicken to a plate and set aside.
In the same skillet, add 1 Tbsp. olive oil and sliced onions and sauté until tender, about 3 minutes.
Add crushed tomatoes with their juice and pour the water or broth. Season with some salt and black pepper. Bring to a boil.
Return the chicken thighs to the skillet and cook on low heat about 10 minutes.
Add the garlic, anchovies, kalamata olives, seasonings, and chopped basil. Stir well and bring to a simmer.
Cover and simmer on medium-low heat until the chicken is cooked, about 10-15 minutes.
Top with fresh basil and enjoy!