Add olive oil to skillet and sear chicken breasts on medium high heat until the bottom is nicely browned then flip and repeat.
Remove from skillet and let rest till cool enough to handle, the inside should still be raw.
Preheat the oven to 400 degrees.
Cut a 2" slit into the side of the chicken breast and use your fingers to open a pocket inside the center of the breasts. Be careful not to tear a hole through.
Mix the pesto and feta together in a small bowl and then fill the chicken breast cavities with the filling.
Use toothpicks to close the hole opening so filling does not leak out during baking.
Rub any remaining mixture on the exterior of the breasts.
Bake in the oven until the internal temperature reaches 165 degrees, about 25 minutes depending on thickness.
Remove toothpicks and serve.
Notes
Note: Cooking time will vary depending on thickness of your chicken breast. Use a meat thermometer to guarantee good results.