Whisk together the coconut aminos, rice vinegar, honey, and tomato paste in a small bowl until the sauce is smooth and well combined.
Pat the chicken breast pieces dry with a paper towel, season with sea salt and black pepper, and toss in a bowl with arrowroot powder until evenly coated.
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 sear for 3-4 minutes per side until golden brown and crispy, then remove the chicken and set it aside on a plate.
In the same skillet, add the red bell pepper, green bell pepper, snap peas, and pineapple chunks, sautéing for 3-4 minutes until the vegetables are tender-crisp.
Return the cooked chicken to the skillet and pour the prepared sauce over the mixture.
Stir constantly for 1-2 minutes until the sauce thickens into a glossy glaze that coats the chicken and vegetables.
Serve the stir-fry immediately over a bed of steamed cauliflower rice.