Make the chicken marinade in a bowl or large zip bag by combining the marinade ingredients. Add the chicken breasts, seal, and refrigerate to marinate for 15-20 minutes.
Position the oven rack in the middle of the oven and preheat it to 400F. Line a baking sheet with parchment paper.
Make the avocado salsa:
While the chicken marinates make the avocado salsa in a medium bowl by combining the avocados, shallot, cilantro, juice of 1 ½ limes, and salt in a bowl. Mix with a fork and refrigerate until ready to use.
Bake the chicken breasts:
Remove the chicken breasts from the marinade and place them on the lined baking sheet. Discard the marinade.
Bake in the preheated oven for approximately 22 minutes, flipping the chicken breasts over after 10 minutes. Continue baking them until the internal temperature reaches 165F. Note: the oven will not brown skinless breasts like a grill. If they're browned, they're overcooked. Remove the pan from the oven.
Serve:
Serve the chicken breasts topped with avocado salsa. Sprinkle with additional chopped cilantro and squeeze a little lime over the top.