In a medium bowl, whisk together honey, lime juice, olive oil, minced garlic, half the salt, and black pepper.
Toss the diced chicken breast in the marinade. Let sit for at least 20 minutes in the refrigerator.
Rinse the jasmine rice under cold water. In a medium saucepan, bring the chicken broth to a boil, add the rice, reduce heat to low, cover, and simmer for 15 minutes.
Heat a large skillet over medium-high heat. Add the marinated chicken (discarding excess marinade) and cook for 6 to 8 minutes until browned and cooked through.
Fluff the cooked rice with a fork. Gently fold in the mashed avocado, chopped cilantro, and remaining salt until the rice is creamy and green.
Divide the avocado rice into bowls and top with the cooked honey lime chicken. Serve immediately.