Lay a chicken breast out flat and sprinkle with salt and black pepper. Spread pesto sauce over the chicken breast and roll the chicken breast in a slice of bacon, securing the roll with toothpicks. Lay the rolled chicken breast into a baking tray. Repeat with remaining chicken breasts. Pour the vegetable oil over the chicken breasts.
Bake in the preheated oven until the chicken is no longer pink inside and the bacon is crisp, about 30 minutes.