For the salsa, mix together in a large bowl: tomatoes, onions, cilantro, chilies, olive oil and lime juice. Cover and refrigerate for about 1 hour. Remove from refrigerator and let it warm to room temperature.
For the fish, rub with olive oil and season with salt and pepper. Cook fish fillets on grill or broiler until tender. (Do not overcook.)
Place fish on a serving plate and place salsa on top of the fish. Garnish with slices of avocado and sprigs of cilantro.