Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and season with salt and pepper. Cook for about 5-7 minutes, or until the chicken is browned on all sides.
Remove the chicken from the skillet and set it aside.
Add the sliced bell peppers and onion to the skillet, and cook for about 3-5 minutes, or until they are softened.
Add the minced garlic and grated ginger to the skillet, and cook for about 1-2 minutes, or until fragrant.
In a small bowl, whisk together the soy sauce, chili garlic sauce, rice vinegar, brown sugar, cornstarch, and water.
Pour the sauce over the vegetables in the skillet, and stir until everything is well combined.
Add the chicken back to the skillet, and stir until it is fully coated in the sauce.
Cook the dish for another 5-7 minutes, or until the chicken is cooked through and the sauce has thickened.
Serve the President's Chicken over rice or noodles, and garnish with chopped green onions, if desired.