Heat olive oil in a large sauté pan over medium heat. Add chicken and sauté until lightly brown and cooked all the way through. Add mushrooms, carrots, water chestnuts, and red pepper and cook until vegetables start to become tender, 5-7 minutes. Add green onion, ginger, and garlic and cook another 2 minutes. Add sesame oil and coconut aminos and let simmer, stirring until the liquid has reduced and slightly thickened 3-5 minutes.