In a large glass measuring cup or bowl, combine the tamari, honey, vinegar, and chili garlic sauce. Set aside.
Heat 1 tablespoon oil in a large skillet or wok over medium-high heat. Lightly season the chicken with salt and pepper. Put the chicken into the skillet in an even layer and let sit undisturbed for 1 minute to sear. Stir fry for 5 more minutes then remove the chicken to a plate or bowl. Add the remaining tablespoon of oil and add the onion, broccoli, and red pepper. Stir fry for 3 minutes or until the broccoli is crisp-tender. Reduce heat to medium. Return the chicken to the skillet, add the sauce, and simmer for another minute or two, stirring often. The chicken and vegetables should be nicely coated, and the sauce is thickened slightly.