Heat the saucepan with olive oil to medium-high heat. Dry chicken with a paper towel. Season on both sides with salt and pepper. Place chicken skin side down in the pan and sear for 3-4 minutes on each side. You may need to do this in batches. Remove the chicken and set them aside. They won't be cooked all the way through.
Lower the heat to medium and add the fennel, leeks, and shallots. Season with salt and pepper and saute until softened, about 8 minutes. Then add the garlic and anchovy paste and saute for another minute or two.
Pour in the red wine and bring to a simmer. Add the chicken thighs back to the pan and simmer all together for 20-25 minutes, or until the chicken thighs reach 165℉.
Remove the chicken thighs and add the butter to the sauce. Stir until combined and spoon the sauce onto the chicken.
Notes
You may need to add a little water to the pan once you add your chicken thighs in if you let the wine reduce too much. The chicken should be about ¼ covered in the sauce while braising.
Trust the anchovy paste. This won't taste like fish but it will make the dish absolutely delicious.