Add the basil, garlic, nuts, cheese, and lemon juice in a food processor and blend until well combined. Slowly drizzle in the olive oil and continue blending until smooth. Season with salt and pepper.
Reserve 1/3 cup pesto and combine the rest with the chicken in a casserole dish or freezer bag. Marinate in the refrigerator overnight.
When ready to eat, preheat a gas or charcoal grill over medium heat. Grill the chicken until cooked through.
Serve the chicken with your favorite side dish and the reserved pesto.