Heat a grill pan to high.
Toast the nuts lightly in small skillet over low heat, then add them to a food processor. Add the arugula, basil, lemon juice, garlic and salt and pepper, to taste, and pulse to combine. With the processor on, stream in the EVOO to form a thick pesto.
Lightly pound out the chicken, then rub all sides with the pesto. Spray the grill pan with cooking spray or rub with a little oil and grill the chicken for 2-4 minutes on each side.