Cook the quinoa according to package directions. Cool after cooking.
Whisk together oils, vinegar, garlic, salt, mustard, oregano, basil and pepper.
Spoon 1/4 cup dressing over chicken and marinate for 20-30 minutes.
Grill chicken or cook in skillet with oil.
Combine cooled quinoa, broccoli, red pepper, olives and dressing.
Serve with grilled chicken.