Blend the basil leaves, garlic and almonds in a blender for 30 seconds. With the motor running, slowly pour 2 tablespoons of the olive oil through the funnel, blending until well combined for about 30 seconds and set aside.
Heat the remaining tablespoon oil in a frying pan and cook the chicken in batches, 3-4 minutes or until golden and set aside.
Add the asparagus stems to the pan and cook, stirring for 2-3 minutes. Add the tips and cook for a further 1-2 minutes.
Stir the basil and almond pesto into the spaghetti. Add the chicken and asparagus.