In mixing bowl, whisk together honey, lime juice, lime zest, minced garlic, ground cumin, salt, and pepper until honey dissolves and mixture is smooth.
Place chicken breasts in resealable plastic bag or shallow dish. Pour marinade over chicken, turning to coat completely. Seal and refrigerate for at least 30 minutes, up to 2 hours.
Rinse jasmine rice under cold water until water runs clear. In medium saucepan, bring chicken broth to boil. Add rice, stir once, cover, and reduce heat to low. Simmer 15 minutes until rice is tender and liquid absorbed.
Remove rice from heat and let sit covered for 5 minutes. Fluff with fork before serving.
Preheat grill or grill pan to medium-high heat. Remove chicken from marinade, letting excess drip off. Place on hot grill.
Grill chicken 6-7 minutes per side, or until internal temperature reaches 165°F (75°C). Watch carefully during last few minutes to prevent honey from burning.
Transfer chicken to cutting board and rest for 5 minutes before slicing on diagonal into 1/2-inch strips.
In bowl, gently combine diced avocado, red onion, cilantro, and olive oil. Mix lightly to keep avocado in chunks.
To assemble: Place serving of rice on plate as base. Top with sliced chicken, then spoon avocado mixture over chicken.
Serve with lime wedges and additional cilantro for garnish.