Place chicken breasts in between 2 sheets of plastic wrap and pound to an even thickness.
Preheat a skillet to medium-high.
Salt and pepper both sides of chicken breasts. Add 2 tbsp oil to the pan.
When the oil is hot swirl it around to cover entire pan. Turn heat to medium. Place chicken in pan and cook for about 5 or 6 minutes per side. Try not to disturb them so they have time to brown on each side.
The chicken should no longer be pink in the middle and reach a temperature of 165°.
Remove the chicken from the pan and cover with foil.
Add 1 tbsp more olive oil and add tomatoes. Cook for a few minutes until they start to burst open. Add 2 tbsp balsamic vinegar. Scrape the bottom of the pan and get up all that goodness.
Add chicken back to pan with the juices.
Top with feta and basil and serve.