In a medium saucepan, bring 1 3/4 cups water and 1/2 tsp. salt to a boil; stir in the rice. Cover, lower the heat and simmer until the liquid is absorbed, about 20 minutes. Let stand, covered, for 5 minutes, then fluff with a fork.
Meanwhile, in a small bowl, combine the pineapple juice, vinegar, soy sauce, 2 tsp. cornstarch, the ketchup and ginger. In a bowl, toss the chicken with the remaining 2 tsp. cornstarch, 1/2 tsp. salt and 1/4 tsp. pepper.
In a large nonstick skillet, heat the oil over medium-high heat. Add the chicken and cook, turning occasionally, until browned, about 5 minutes; transfer to a plate. Add the bell pepper and cook, stirring, until crisp-tender, about 2 minutes. Stir in the pineapple chunks and reserved chicken.
Whisk the pineapple juice mixture into the chicken mixture and cook, stirring occasionally, until the sauce has thickened and the chicken is cooked through, about 2 minutes. Serve over the rice.