Place the chicken breasts in a large bowl. In a blender or food processor, combine the lime juice, cilantro, mustard, olive oil, cumin, salt, pepper, and cayenne (if using). Pulse to combine well. Pour over the chicken and toss to coat. Cover and refrigerate for at least 1 hour or up to 4 hours.
Preheat the oven to 400ºF. Remove the chicken from the marinade. Place in a baking dish and bake for 25-30 minutes or until meat registers 165ºF on an instant-read thermometer. Serve with the salsa.