In a medium bowl, combine the diced mango, pineapple, soy sauce, honey, olive oil, minced garlic, grated ginger, black pepper, salt, and lime juice. Mix well to create a marinade.
Place the chicken breasts in a resealable plastic bag or shallow dish and pour the marinade over them. Seal the bag or cover the dish and refrigerate for at least 1 hour, or up to 4 hours for more flavor.
Preheat the grill to medium-high heat. Remove the chicken from the marinade, allowing excess marinade to drip off.
Grill the chicken for about 6-7 minutes per side, or until the internal temperature reaches 165°F and the chicken is cooked through.
While the chicken is grilling, you can also grill any remaining pineapple and mango pieces for added flavor, about 2-3 minutes per side.
Once cooked, remove the chicken from the grill and let it rest for 5 minutes. Slice the chicken and serve it topped with the grilled fruit and garnished with fresh cilantro.