In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced bell pepper and onion. Stir-fry for about 3-4 minutes until they are slightly tender.
In a mixing bowl, combine the reserved pineapple juice, sugar, white vinegar, ketchup, and soy sauce. Stir until the sugar is dissolved.
Pour the sweet and sour sauce mixture into the skillet with the cooked vegetables. Bring to a simmer, stirring occasionally.
In a small bowl, mix the cornstarch and water to create a slurry. Gradually add the slurry to the sauce, stirring constantly until the sauce thickens.
Return the cooked chicken and pineapple chunks to the skillet, mixing everything well to coat with the sauce. Heat through for an additional 2-3 minutes.
Season with salt to taste and serve the sweet and sour chicken over cooked rice.