In a medium bowl, combine strawberries, onion, lime juice, feta and olive oil. Set aside
Preheat grill or grill pan to medium heat. In a large bowl, whisk together 1 Tbsp olive oil and 2 tsp lime juice and season with salt and pepper. Add chicken breasts and toss to coat. Grill chicken for 6 minutes per side or until meat thermometer reads 165°F. Loosely cover chicken with foil and let rest for 5 minutes.
Add chopped avocado to salsa and season with salt and pepper; toss gently. Top chicken with salsa to serve.