In a small bowl whisk together lime juice, olive oil, honey, salt to taste and ceyenne pepper.
Pour half of mixture over chicken in resealable plastic bag, saving remaining mixture for later. place bag of chicken in fridge for 1 hour.
Spray cold grill rack with nonstick cooking spray and preheat grill to medium heat.
Remove chicken from bag and discard marinade from bag. Place chicken on grill, cover with lid and cook 8 to 10 minutes on each side or until tender and no longer pink.
Chop into pieces. Then, combine chicken pieces, avocados, tomatoes, cucumber and basil in large salad bowl.
Toss gently with reserved lime mixture and serve.