In a large bowl, toss chicken with 1 tablespoon each soy sauce and cornstarch, salt, and pepper. In another bowl, combine remaining soy sauce and cornstarch, vinegar, ketchup, sugar, and 1/2 cup water; set aside.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high. Cook half the chicken, turning occasionally, until browned and almost cooked through, 4 minutes; remove. Cook the remaining chicken in another tablespoon oil; remove.
Add remaining oil to the pan. Add peppers, white parts of scallions, and garlic; cook over medium-high, stirring, until peppers are crisp-tender, about 3 minutes.
Whisk soy sauce mixture; add to pan. Return chicken; add scallion greens. Cook, stirring, until sauce has thickened and chicken is cooked through, about 2 minutes. Serve immediately over rice, if desired.
Cut the vegetables ahead of time; refrigerate, in separate airtight containers lined with damp paper towels, for up to a day. For sweeter flavor, add up to a cup of cubed pineapple along with the scallion greens in step 4.