Preheat a grill or a grill pan to medium-high. Preheat the oven to 375 degrees and cook the bacon on a broiler pan in the oven for 20 minutes. (To get the bacon extra-crisp, don't open the oven to check on it too often-you'll let the heat out.) Drain the bacon on paper towels, then chop it.
Coat the chicken with EVOO and grill seasoning. Grill the chicken until cooked through, 3 to 4 minutes on each side.
Combine the lettuce and tomatoes in a large bowl. Cut the avocado in half, pit it and spoon the flesh into a food processor bowl. Add the onion, garlic, lemon juice, jalapeno and cilantro to the avocado. Turn the processor on and add 1/3 cup of the EVOO in a thin stream; process until smooth. season to taste with salt.
Chop the chicken into pieces and arrange on the salad. Pour the dressing over the salad, then scatter the bacon across the top.