Preheat the oven to 375. Mix the nuts in a pie plate with 1/2 tsp salt and 1/2 tsp pepper. Press the chicken into the nuts. Heat 1 Tbs of the oil in a skillet and cook the breasts, 2 min per side. Place the breasts in a baking dish and bake for 15 min or til thermometer registers 160 and juices run clear.
Heat the remaining Tbs of oil in a nonstick skillet over high heat. Add the diced onion, 1/4 tsp salt, and a pinch of pepper. Cook til the onion is browned.
Line 4 serving plates with lettuce. Slice the chicken breasts and arrange 1 breast on top of the lettuce on each place. Serve with the dressing.
To make the dressing:
Puree the onion, avocado, oil, lime juice, and water in a blender.