Pat the chicken breast dry with paper towels and toss the cubes in a bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
Heat the avocado oil in a large non-stick skillet or wok over medium-high heat.
Add the chicken to the skillet and cook for 5-6 minutes, turning occasionally, until the exterior is golden brown and crispy; remove chicken from the pan and set aside.
In the same skillet, add the bell pepper, broccoli, and snap peas with a tablespoon of water, covering for 2 minutes to steam-fry until tender-crisp.
While the vegetables cook, whisk together the coconut aminos, rice vinegar, pineapple juice, minced ginger, and minced garlic in a small bowl.
Return the crispy chicken to the skillet and pour the sauce over the mixture, tossing constantly for 1-2 minutes until the sauce thickens into a glossy glaze.
Serve the stir-fry immediately over the warm cooked brown rice.