Cut the chicken breast into bite-sized pieces and toss in a bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
In a small glass jar or bowl, whisk together the coconut aminos, rice vinegar, pineapple juice, minced ginger, and minced garlic to create the sauce.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet in a single layer and cook for 5-6 minutes, turning occasionally, until the edges are golden brown and the meat is cooked through.
Remove the chicken from the skillet and set aside on a plate.
Add the red bell pepper, broccoli, and snap peas to the same skillet, sautéing for 3-4 minutes until they are tender-crisp and bright in color.
Return the cooked chicken to the skillet and pour the prepared sauce over the chicken and vegetables.
Stir constantly for 1-2 minutes until the sauce bubbles and thickens into a glossy glaze.
Serve the hot stir-fry immediately over the warm cooked brown rice.