Combine all Fiesta Lime Rub ingredients in a bowl and massage evenly over the chicken breasts.
If possible, let the chicken marinate at room temperature for 30 minutes or refrigerate for up to 8 hours, then bring to room temp before cooking.
Begin prepping the Avocado Salsa while the chicken marinates.
For stovetop cooking, warm a greased grill pan or skillet over medium-high heat until hot.
Add the chicken without moving it and cook for 3 to 5 minutes until it develops a nice brown crust.
Flip the chicken, cover, lower heat to medium, and cook another 5 to 7 minutes until fully cooked.
Remove chicken, let rest for 5 minutes before slicing, and optionally squeeze fresh lime over the top.
For grilling, preheat and grease grill to medium heat (375-450°F).
Place chicken on grill and cook without turning for 5 to 7 minutes, then repeat on the other side until internal temp reads 165°F.
Take off grill and allow the chicken to rest 5 minutes before slicing.
To prepare Avocado Salsa, mix all ingredients except avocados in a large bowl.
Cover and chill the salsa mixture anywhere from 30 minutes up to 24 hours.
When ready to serve, fold in chopped avocados gently.
Adjust seasoning with extra salt, pepper, and jalapeno seeds to your preferred heat level.