Vinaigrette:
Combine all the ingredients in a blender or food processor and blend until smooth. Season to taste. Set aside until ready to use.
Chicken:
Season the chicken with salt and pepper.
In a large skillet, melt 4 tablespoons of butter and 2 tablespoons olive oil. When the oil shimmers, add the chicken and cook 3-4 minutes per side or until internal temperature reaches 165ºF.
Add remaining butter, garlic, and tomatoes, quickly baste the chicken and tomatoes with the butter. Remove pan from heat. Squeeze in lemon juice.
Garnish chicken with fresh basil leaves and serve with vinaigrette. Enjoy!