Heat the oil in a large skillet over medium heat. Add the onion and cook, stirring, for 2 minutes. Add the chicken and cook until golden brown on all sides, about 5 minutes.
In a blender, combine the pesto ingredients and process until smooth, adding more oil if necessary to create a sauce-like consistency.
Add the sauce to the chicken in the skillet and cook for 1 minute to heat through. Serve the chicken and sauce over the pasta.