Pat the chicken dry and cut into bite-size pieces; season with a pinch of salt if desired.
In a small bowl, whisk together the soy sauce, water or chicken stock, rice vinegar, and cornstarch until smooth; set aside.
Heat 1 tablespoon of olive oil in a large skillet or wok over medium heat. Add the chicken and cook, stirring occasionally, until no longer pink and cooked through, about 5–7 minutes. Transfer the chicken to a plate and set aside.
Add the remaining 1 tablespoon olive oil to the same pan. Add the grated ginger and minced garlic and sauté for about 1 minute, until fragrant.
Add the black pepper and sauté for about 3 minutes, then add the sliced onion, chopped celery, and sliced green bell pepper. Cook until vegetables are tender-crisp, about 3–5 minutes.
Return the cooked chicken to the pan, pour in the prepared sauce, sprinkle in the 1/4 teaspoon salt, and stir to combine. Simmer until the sauce thickens and coats the chicken and vegetables, about 1–2 minutes.
Serve hot with rice.