Toss the chicken breasts with the salt, pepper and 1 tablespoon olive oil in a small bowl. Set aside.
Heat a medium Dutch oven over medium heat. Add 2 tablespoons olive oil to the pan and heat an additional 30 seconds. Add the onion, garlic and fennel to the hot pan. Season with salt and stir with a wooden spoon to combine. Cook, stirring often, until the vegetables are beginning to soften and are fragrant, about 3 minutes. Add the oregano and garlic powder to the vegetables and stir to combine. Continue to cook until the vegetables are translucent and beginning to brown slightly, another 3 to 4 minutes. Add the tomatoes to the pan along with the vinegar. Bring the mixture to a simmer. Reduce the heat to maintain a gentle simmer. Using the back of a wooden spoon, crush the tomatoes into medium-sized pieces. Simmer for 10 minutes while you start the chicken.
Meanwhile, heat a medium skillet over medium-high heat. Add the remaining tablespoon olive oil and heat an additional 30 seconds. Add the chicken to the hot skillet and cook, undisturbed, until deep golden brown, 3 to 4 minutes. Flip the chicken and cook until the chicken is evenly browned on both sides, an additional 3 to 4 minutes. Carefully ladle the tomato mixture over and around the chicken, then reduce the heat to maintain a gentle simmer and continue to cook for an additional 5 minutes. Stir in the chickpeas and butter and cook to heat through, 2 more minutes. Did you taste it? Season with additional salt, garlic powder or garlic salt if needed. Stir in the basil and serve topped with Parmesan, if desired.