Cut chicken breasts into 1 inch pieces. Heat 1 tbs. oil in large deep skillet, pan or dutch oven.
Add cut chicken to skillet and cook at medium heat. Stir meat often to cook thoroughly, about 5-7 minutes, until juices run clear. Remove chicken from skillet, add to seperate bowl. Drain juices from skillet.
Heat remaining oil in skillet. Stir-fry onion on medium heat for 3-4 minutes, just until crisp-tender. Add in peppers and cook for another 2-3 minutes. Remove vegetables from pan; add to chicken.
Increase heat to medium-high. Mix together brown sugar and cornstarch in skillet. Stir in pineapple with juice, vinegar and soy sauce. Heat to boiling, stirring constantly until sauce is thickened and bubbling; reduce heat to simmer.
Add chicken and vegetables, stir to cover in sauce. Simmer on low until heated through. Serve over white or brown rice.