To begin, juice one of the limes into a small mixing bowl. Add in the tequila, water, grated garlic, 1/2 tsp salt, and 1/4 tsp pepper. Whisk these together.
Place the chicken in a quart sized zip-lock bag. Pour the marinade into the bag. Carefully remove as much air as possible and close. Marinate this in the refrigerator for 1 hour.
Meanwhile, place a sieve over a mixing bowl. Peel the oranges and cut the flesh into 3/4 inch pieces, placing them into the sieve as you go. The excess juice from the oranges will drain down into the bowl.
When no more juice drains, set the oranges aside.
To the orange juice, add the extra virgin olive oil, honey, cayenne pepper, and the remaining 1/4 tsp salt and 1/4 tsp black pepper.
With a microplaner, zest one of the remaining limes, giving you a teaspoon of fine lime zest. Add that to the mixture in the bowl. Juice the two limes and add the juice as well.
Whisk everything together and set it aside for now.
Heat your oven to 425 degrees.
Place the chicken strips on a baking sheet, allowing the excess marinade to drip back into the bag.
Bake the chicken for 15-20 minutes or until cooked through.
Cut the chicken cross-ways into 1/2 inch slices.
In a large bowl, combine the lettuce and orange chunks.
Give the dressing a quick whisking and pour over the salad. Toss to coat.
Halve, pit, and slice the avocados.
To serve, place some of the salad mixture on your dinner plate. Top with the chicken and garnish with avocado slices.