In a large skillet over medium high heat, add oil and saute chicken until cooked through. Season with salt and pepper to taste.
Meanwhile, combine quinoa with 2 cups water in a medium saucepan and bring to a boil. Reduce to a simmer, and cook for about 15 minutes or until the grains are tender and all of the liquid has absorbed.
To make the basil pesto vinaigrette, combine basil, olive oil, vinegar, lemon juice, garlic and pine nuts in a food processor or blender, and blend until smooth. Season with salt and pepper to taste.
To assemble, divide cooked quinoa into two bowls and arrange chicken, red peppers, avocado, and toasted pepitas on top. Drizzle with vinaigrette and serve warm or cold.