Dice the chicken breast into 1-inch cubes and toss in a bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
In a small jar or bowl, whisk together the honey, rice vinegar, tomato paste, tamari, minced ginger, and minced garlic to create the sweet and sour sauce.
Heat the avocado oil in a large skillet or wok over medium-high heat and sear the chicken until golden and crispy on all sides, about 6 to 8 minutes.
Remove the chicken from the pan and set aside, then add the sliced bell peppers, snap peas, and red onion to the same skillet.
Sauté the vegetables for 3 to 4 minutes until they are tender-crisp, then return the chicken to the pan.
Pour the sauce over the chicken and vegetables, tossing for 1 to 2 minutes until the glaze thickens and coats everything, then serve over warm brown rice.