In a shallow bowl, beat eggs. Add 1/2 cup cornstarch to another bowl.
Heat 3T oil in a large frying pan over medium heat. Dip the chicken pieces in egg, then coat evenly with cornstarch, shaking off any excess. Place in the frying pan. Repeat with remaining chicken.
Pan fry the chicken until golden on the outside, turning as necessary (minimally). Chicken does not have to be cooked through. Remove from pan and set aside.
Combine ketchup, soy sauce and vinegar in a small saucepan over medium heat. Whisk cornstarch into the reserved pineapple juice, then add to the pan. Simmer until slightly thickened; remove from heat.
Dump all but 1 T oil (or add more oil to equal 1 T). Add the bell peppers and onion to the pan and saute over high heat until they begin to soften. Add the pineapple and cook until they begin to caramelize.
Return the chicken to the pan and pour sauce over. Toss until chicken and vegetables are evenly coated, saute until chicken is cooked through, approximately 3-5 minutes. Serve with white rice.