Preheat the oven to 350 degrees. Heat a ceramic coated dutch oven over medium/high heat. Add the butter and melt. Sprinkle salt and pepper over both sides of the chicken.
Add the chicken to the hot butter, skin side down. Let chicken cook for a few minutes, until a deep, golden brown. Flip chicken over and brown the other side as well. Remove the chicken thighs from the pan and set aside.
Add the garlic and oregano and sauté for 30 seconds. Pour in the chicken broth and lemon juice. Bring to a boil and stir for one minute to deglaze the pan. Add the chicken thighs back into the pan and pour the coconut milk over the top. Bring to a boil and turn off the stove. Place the dutch oven in the preheated oven and bake for an additional 50-60 minutes (40-50 minutes if boneless, skinless) until internal temperature reads 165°F.
Chicken skin should be crispy and meat tender when chicken is done. Place chicken on a platter. Taste the sauce and add more salt, if needed. Pour sauce over chicken and garnish with fresh oregano and lemon slices.