Dice the chicken breast into 1-inch cubes and toss in a bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
Heat sesame oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and cook until golden brown and crispy on all sides, about 6-8 minutes.
Remove the chicken from the pan and set it aside on a plate.
In the same pan, add the sliced bell peppers, snap peas, minced ginger, and minced garlic, sautéing for 3-4 minutes until tender-crisp.
In a small bowl, whisk together the coconut aminos, rice vinegar, and honey to create the glaze.
Return the chicken to the pan and pour the glaze over the mixture, tossing constantly until the sauce thickens and coats everything.
Serve the stir-fry immediately over the warm, cooked brown rice.