Make the sauce: In a small bowl, whisk the soy sauce, barbecue sauce, sesame oil, clove of garlic, brown sugar, and corn starch. Set aside.
Rinse and drain the Shirataki noodles well. Press them dry with a paper towel to get as much moisture out as possible. This will help to ensure the sauce sticks to them and doesn’t slip off.
In a large nonstick skillet, heat 2 teaspoons of the vegetable oil over medium-high heat. Add the chicken and cook, stirring occasionally, until browned and cooked through, about 6 minutes. Transfer to a clean plate and wipe out the pan with paper towels.
Return the pan to medium-high heat (turning it down if it begins to smoke) and add the remaining teaspoon of oil. Add the celery, bell pepper, and scallions, and cook, stirring frequently, until tender-crisp, about 3 minutes. Return the cooked chicken to the pan. Add the Shirataki noodles and the soy sauce mixture, tossing to coat all ingredients well, and let the pan cook until the sauce has thickened, about 2 minutes.