Preheat oven to 425F. Line a baking sheet with foil; set aside. Halve peppers lengthwise. Remove stems, seeds, and membranes. Place pepper halves, cut sides down, on the prepared baking sheet. Roast peppers in the preheated oven for 20 to 25 minutes or until skins are blistered and dark. Carefully fold foil up and around pepper halves to enclose; let stand about 15 minutes. Use a sharp knife to loosen the edges of the skins; gently and slowly pull off the skin in strips. Discard skins. Cut peppers into bite-size strips. Set aside.
In a fine-mesh sieve thoroughly rinse the quinoa with cold water. In a medium saucepan combine quinoa and the 1 cup water. Bring to boiling; reduce heat. Simmer, covered, for 25 minutes. Remove from heat. Uncover and let stand about 30 minutes.
For dressing, in a small screw-top jar combine lime juice, olive oil, garlic, salt, and black pepper. Cover and shake well to combine.
In a large bowl combine roasted pepper strips, qinoa, chicken, cilantro, green onion, pine nuts. Drizzle with dressing and toss to combine. Line serving plates with lettuce. Top with quinoa mixture. Serve salad at room temperature. Makes 4 or 5 main-dish servings.