In a small bowl, whisk together the coconut aminos, honey, minced ginger, minced garlic, and arrowroot powder to create the teriyaki sauce.
Cut the chicken breast into 1-inch bite-sized cubes and season evenly with sea salt and black pepper.
Heat the sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken cubes to the skillet and sear until golden brown and cooked through, approximately 5 to 6 minutes.
Remove the cooked chicken from the skillet and set it aside on a plate.
Add the broccoli florets, sliced red bell pepper, and snap peas to the same skillet with a tablespoon of water.
Cover the skillet and steam the vegetables for 2 minutes until they are tender-crisp and bright in color.
Return the chicken to the skillet and pour the prepared teriyaki sauce over the chicken and vegetables.
Toss the mixture constantly for 1 to 2 minutes until the sauce thickens into a glossy glaze that coats every ingredient.
Serve the hot stir-fry immediately over the portion of warm cooked brown rice.