In a medium sized bowl whisk together the soy sauce, rice vinegar, sesame oil, salt and pepper. Add chicken to the marinade, tossing to coat. Cover and refrigerate the chicken in the marinade for at least 15 minutes or even a few hours.
While the chicken is marinating prepare stir-fry sauce, whisking all the ingredients together.
Preheat a large skillet or wok over high heat. When the skillet is hot add in a couple teaspoon of oil and then the chopped broccoli florets. Stir-fry the broccoli for about 2 minutes, until it is bright green, but still crisp. Remove the broccoli from the skillet onto a plate.
Add another teaspoon or so of oil to the skillet then add in the chicken, leaving the liquid from the marinade in the bowl. Stir fry the chicken until it is cooked through, about 3 minutes, then add the broccoli back in.
Pour the stir fry sauce in with the chicken and broccoli and stir it around until it starts to thicken and coat everything, about 2-3 minutes.
Remove the stir fry from the heat and serve over quinoa or rice.