Pat the chicken breast dry with paper towels and cut into bite-sized pieces, then season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the fresh orange juice, coconut aminos, raw honey, grated ginger, minced garlic, and arrowroot powder until the starch is fully dissolved.
Heat the avocado oil in a large non-stick skillet or wok over medium-high heat until shimmering.
Add the chicken pieces to the skillet in a single layer and sear undisturbed for 3 minutes to develop a golden crust, then toss and cook for another 2-3 minutes until cooked through.
Transfer the seared chicken to a plate and set aside.
Add the broccoli florets to the same skillet with two tablespoons of water; cover with a lid and steam for 2-3 minutes until they are bright green and tender-crisp.
Remove the lid and return the chicken to the skillet, tossing it with the broccoli.
Give the orange sauce a quick whisk and pour it into the skillet, stirring constantly for 1 minute as the sauce bubbles and thickens into a glossy glaze.
Serve the orange chicken and broccoli immediately over the warm cooked brown rice.