Cut the chicken into 1-inch cubes and add to a zip-top bag with the gluten free soy sauce, rice vinegar, and cornstarch. Toss to coat and set aside.
Slice the red bell pepper, cut the broccoli into florets, and drain the baby corn and water chestnuts.
Heat a large skillet or wok over medium-high heat with oil. Add the chicken in a single layer and cook until lightly browned and cooked through to 165 degrees F. Transfer to a plate.
Add more oil to the pan, then add the bell pepper and broccoli. Cook until beginning to soften, then stir in the sugar snap peas, baby corn, and water chestnuts. Cook until crisp-tender.
Return the chicken and any juices to the pan. Pour in the stir fry sauce and stir to coat. Simmer briefly until slightly thickened.
Remove from heat and garnish with green onion tops and sesame seeds. Serve over rice, gluten free noodles, or enjoy plain.