Cut the chicken breast into bite-sized pieces and toss in a bowl with the arrowroot powder, sea salt, and black pepper until evenly coated.
Heat the avocado oil in a large skillet or wok over medium-high heat.
Add the chicken to the pan and sear for 5-6 minutes, turning occasionally, until golden brown and cooked through; remove chicken from the pan and set aside.
In the same pan, add the broccoli florets, sliced bell pepper, and snap peas, sautéing for 3-4 minutes until they are tender-crisp and bright.
While the vegetables cook, whisk together the honey, tamari, minced garlic, and grated ginger in a small bowl.
Return the cooked chicken to the skillet with the vegetables and pour the honey-garlic sauce over the top.
Toss everything together for 1-2 minutes until the sauce thickens into a glossy glaze that coats every piece.
Serve the stir-fry immediately over the warm cooked brown rice.