Season the chicken breasts all over with salt and pepper. Add the flour to a shallow bowl or plate. Dredge the chicken by placing it in the flour, then turning to coat all sides evenly.
4 ea Boneless, skinless chicken breasts, 1/2 cup Flour
Heat 4 tablespoons of butter and the olive oil in a medium skillet over medium. When the mixture is bubbling, shake off any excess flour from the chicken and add to the skillet. Cook, undisturbed, until golden brown, about 4 minutes. Flip the pieces over and continue cooking until cooked through, about 4 more. Transfer the chicken to a plate.
4 Tbsp Butter, 2 Tbsp Olive oil
Add the shallots to the pan and cook, stirring, until softened and lightly caramelized, about 2 minutes. Stir in the tomatoes. Simmer until the sauce is reduced by about half, about 3 minutes.
1 ea Shallot, diced, 24 oz Tomatoes, chopped
Stir in the capers, butter and the vinegar. Turn off the heat and season with salt.
2 Tbsp Capers in brine, drained, 2 Tbsp Butter, 1 tsp Red wine vinegar
To serve, top the chicken with the basil leaves and the tomato sauce and season with black pepper.
Plenty of Basil leaves, torn