Zest and juice one lime into large bowl for marinade. Zest and juice second lime into medium bowl for salsa. Add half of chopped jalapeno, half of chopped onion and half of chopped cilantro to each bowl.
Add olive oil, salt and pepper to the large bowl for the marinade and whisk together. Add chicken breasts and toss to coat. Marinate for 30 minutes.
Add mango, avocado, cilantro, and salt to bowl for salsa. Toss and set aside.
Grill chicken 4-5 minutes per side, on a pre-heated grill over medium heat. Remove from grill and cover with foil to rest for 5 minutes. Serve with salsa.