Preheat the air fryer to 375°F (190°C) for 5 minutes.
Pat the chicken breasts dry with paper towels.
Brush both sides of the chicken breasts with 1 tablespoon olive oil.
Season both sides evenly with 1/2 teaspoon salt, 1/4 teaspoon black pepper, and 1/4 teaspoon garlic powder.
Place the chicken breasts in the air fryer basket in a single layer.
Cook for 9 minutes, then flip the chicken breasts and cook for an additional 9 minutes or until the internal temperature reaches 165°F (74°C).
While the chicken is cooking, prepare the pesto: In a food processor, combine 1 cup fresh basil leaves, 1/4 cup grated Parmesan cheese, 1/4 cup pine nuts, and 1 minced garlic clove.
Pulse until coarsely chopped.
With the processor running, slowly drizzle in 1/3 cup extra virgin olive oil until the mixture is smooth and emulsified.
Add 1/2 teaspoon lemon juice and pulse once to combine.
Remove the chicken breasts from the air fryer and let them rest for 3 minutes.
Slice the chicken breasts and spoon the fresh pesto generously over the top before serving.