Cut the chicken into bite-size pieces and season lightly with pepper.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat and add the chicken, stirring to coat.
Cook the chicken, stirring often, for 5–7 minutes until cooked through.
While the chicken cooks, spiralize the zucchini and set the zoodles aside; chop scallions if using.
In a small bowl, whisk together 2 tbsp brown sugar, 2 tbsp soy sauce, 2 tbsp honey, 1 minced garlic clove, and 2 tbsp water to make the teriyaki sauce.
In another small bowl, mix 1 tablespoon cornstarch with 2 tablespoons cold water until smooth.
Reduce the skillet heat to medium and pour in the teriyaki sauce, then add the cornstarch mixture and stir to coat the chicken; let it simmer and thicken for 1–2 minutes.
Add the zucchini noodles to the skillet and toss with tongs to combine with the sauce and chicken, cooking just 1–2 minutes until warmed through but still firm.
Serve immediately, sprinkled with chopped scallions if desired.