Preheat oven to 350 degrees F (175 degrees C).

Bring rice and water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover, and simmer until rice is tender and the liquid has been absorbed, 20 to 25 minutes.

Heat oil in a large skillet over medium-high heat. Brown chicken breasts on both sides, about 2 minutes per side.

Combine apricot jam, Italian-style salad dressing, and dried onions together in a bowl. Place browned chicken in a baking dish and pour jam mixture over the chicken; bake for 15 minutes. Add the pineapple, chopped onion and chopped red bell pepper; continue baking until chicken is cooked through and no longer pink inside, another 15 minutes. Serve over cooked rice.