Place the chicken thighs in the slow cooker. In a small bowl, stir together the honey, soy sauce, and minced garlic until combined. Pour the mixture over the chicken.
Cover and cook on low for 5 hours. The chicken should become very tender.
Add the broccoli florets to the slow cooker, nestling them around the chicken. Continue cooking on low for 1 more hour.
While the broccoli cooks, combine the rice, water, and salt in a saucepan. Bring to a boil, then reduce to a simmer, cover, and cook for 18 minutes until the water is absorbed.
Fluff the rice with a fork. Serve the chicken thighs and broccoli over the rice, spooning some of the sauce from the slow cooker on top.