In a blender, puree until smooth the jalapeno pepper, garlic, vegetable oil, tomato paste, salt, honey and lime juice. Pour marinade over the chicken. Add the lime zest and toss to coat. Cover with plastic wrap and refrigerate overnight.
Preheat boiler to medium heat.
Arrange chicken on a baking sheet lined with parchment paper. Broil chicken at least 6 inches from the heat for 4 to 5 minutes per side; or until chicken is crispy on the outside and cooked through. Serve with Avocado Dip.
Pit and peel avocado. Place avocado in a medium bowl; mash. Fold in 3 tablespoons chopped fresh cilantro leaves; lime juice, garlic and salt; and freshly ground black pepper, to taste.