Cut the chicken breast into bite-sized pieces and pat them thoroughly dry with a paper towel.
In a medium bowl, toss the chicken pieces with arrowroot powder, sea salt, and black pepper until evenly coated.
Heat the avocado oil in a large stainless steel or cast iron skillet 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 cooked through, then remove and set aside.
Add the toasted sesame oil to the same skillet and toss in the broccoli florets and sliced red bell peppers.
Sauté the vegetables for 3-5 minutes, stirring frequently, until they are vibrant in color and crisp-tender.
In a small glass jar, whisk together the fresh orange juice, coconut aminos, grated ginger, and minced garlic.
Return the cooked chicken to the skillet with the vegetables and pour the orange sauce over everything.
Stir-fry for 1-2 minutes until the sauce bubbles and reduces into a thick, glossy glaze that coats every piece.
Transfer the stir-fry to a bowl and serve immediately over the warm cooked brown rice.