In a large skillet over medium-high heat, heat oil. Season chicken with garlic powder and pepper and cook until golden and cooked through, 6 to 8 minutes per side, turning every 3 to 4 minutes. Transfer to a plate.
Add balsamic vinegar to skillet, then add garlic and cook until fragrant, 1 minute. Add tomatoes and let simmer until soft, 5 to 7 minutes.
Return chicken to skillet and nestle in tomatoes. Top each chicken thigh with burrata pieces and fresh basil and cover with a lid to melt. Spoon tomatoes and balsamic mixture over chicken and serve.