Heat oil in a large skillet over medium-high heat. Add chicken and cook until golden brown, about 5 minutes per side. Add tomato sauce mixture and bring to a boil. Reduce heat to medium-low, cover, and simmer until chicken is no longer pink in the center and the juices run clear, about 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).