Remove moisture from the chicken thighs with a paper towel and generously season with salt and black pepper.
Heat oil in a large cast iron or non-stick skillet over medium-high heat. When the oil starts to shimmer, place the chicken thighs skin-side down and cook (do not move them) until they're nicely browned, about 4 to 5 minutes. Flip the thighs and cook for an additional 4 to 5 minutes. Remove the chicken from the skillet and set aside on a plate.
In the same pan, add the garlic, anchovies, and red pepper flakes. Cook, stirring occasionally, until the garlic is fragrant and the anchovies have melted into the mix, roughly 2 minutes.
Stir in the tomato paste and dried oregano with the garlic and cook for an additional minute. Add the tomatoes and stir to combine with the tomato paste.
Next, add in 2 Tablespoons capers and olives followed by the chicken thighs. Partially cover and simmer for 15 to 20 minutes or until the chicken has reached 165F and is cooked through.
Taste and adjust seasonings. Top with remaining 1 Tablespoon capers.
Remove from the heat and, if desired, garnish with Italian parsley, Kalamata olives and cracked pepper.
Store leftovers in an airtight container in the fridge for up to 3 days.